Branching laws: Restriction of unitary representations, discretely decomposable restrictions, estimates of multiplicities

[P] T. Kobayashi, Admissible restrictions of irreducible representations of reductive Lie groups: Symplectic geometry and discretely decomposability, preprint, 20 pages. arXiv: 1907.12964.
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[P] T. Kobayashi, Branching laws of unitary representations associated to minimal elliptic orbits for indefinite orthogonal group O(p,q), preprint, 37 pages.
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[P] T. Kobayashi and B. Speh, Distinguished representations of SO(n+1,1) ×SO(n,1), periods and branching laws, preprint, 32 pages.
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[P] T. Kobayashi and M. Pevzner, Inversion of rankin-cohen operators via holographic transform, preprint. 52 pages. arXiv: 1812.09733.
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[279] T. Kobayashi, Recent advances in branching laws of representations [hyogen no bunki-soku no saikin no shinten], Sugaku 71 (2019), no. 4, 388-416 (Japanese).
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[277] T. Kobayashi, Conformal symmetry breaking on differential forms and some applications, Geometric Methods in Physics XXXVI workshop 2017 (P. Kielanowski, A. Odzijewicz, and E. Previato, eds.), Trends in Mathematics, Birkhäuser, Cham, 2019, pp. 289-308, DOI: 10.1007/978-3-030-01156-7_32. arXiv: 1712.09212.
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[275] T. Kobayashi and B. Speh, Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad, SSTF 2016: Geometric Aspects of the Trace Formula (W. Müller, S. Shin, and N. Templier, eds.), Simons Symposium on the Trace Formula, Springer, Cham, 2018, pp. 245-266, Published online: 12 October 2018. Print ISBN: 978-3-319-94832-4. Online ISBN: 978-3-319-94833-1. arXiv: 1702.00263. DOI: 10.1007/978-3-319-94833-1_8.
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[272] T. Kobayashi and A. Leontiev, Image of conformally covariant, symmetry breaking operators for Rp,q, Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics. Volume 1. LT-XII/QTS-X 2017 (V. Dobrev, ed.), Springer Proceedings in Mathematics & Statistics, vol. 263, 2018, pp. 3-31, DOI: 10.1007/978-981-13-2715-5_1.
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[271] T. Kobayashi, Residue formula for regular symmetry breaking operators, Contemporary Mathematics, vol. 714, pp. 175-193, Amer. Math.Soc., 2018, arXiv: 1709.05035. 10.1090/conm/714/14380.
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[270] T. Kobayashi, Symmetry breaking operators for orthogonal groups O(n,1), Mathematisches Forschungsinstitut Oberwolfach Report (2017), no. 25, 1572-1575, DOI: 10.4171/OWR/2017/25. Harmonic Analysis and the Trace Formula, Organised by Werner Müller, Sug Woo Shin, Birgit Speh, and Nicolas Templier.
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[269] T. Kobayashi and S. Nasrin, Geometry of coadjoint orbits and multiplicity-one branching laws for symmetric pairs, Algebras and Representation Theory 21 (2018), no. 5, 1023-1036, Special Issue: Representation Theory at the Crossroads of Modern Mathematics - Special volume in honor of Alexandre Kirillov. DOI: 10.1007/s10468-018-9810-8.
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[268] T. Kobayashi and B. Speh, Symmetry breaking for representations of rank one orthogonal groups II, Lecture Notes in Mathematics, vol. 2234, Springer, 2018, eBook:978-981-13-2901-2. arXiv: 1801.00158. DOI: 10.1007/978-981-13-2901-2.
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[266] T. Kobayashi, T. Kubo, and M. Pevzner, Conformal symmetry breaking operators for anti-de Sitter spaces, Geometric Methods in Physics XXXV (P. Kielanowski, A. Odzijewicz, and E. Previato, eds.), Trends in Mathematics, Birkhäuser, Springer, 2018, pp. 75-91, DOI: 10.1007/978-3-319-63594-1_9. arXiv: 1610.09475.
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[258] T. Kobayashi, Global analysis by hidden symmetry, Progr. Math., 323 (2017), pp. 359-397, a special issue in honour of Roger Howe for his 70th birthday. DOI: 10.1007/978-3-319-59728-7_13. arXiv: 160808356.
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[256] T. Kobayashi and A. Leontiev, Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups O(p,q), Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 8, 86-91, DOI: 10.3792/pjaa.93.86.
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[254] T. Kobayashi and A. Leontiev, Symmetry breaking operators for conformal transformation groups o(p,q), Abstract Book of MSJ Spring Meeting 2017 at Tokyo Metropolitan University, 2017, pp. 81-82 (Japanese).
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[250] T. Kobayashi, T. Kubo, and M. Pevzner, Conformal symmetry breaking operators for differential forms on spheres, Lecture Notes in Mathematics, vol. 2170, Springer Singapore, 2016, ix+192 pages. DOI: 10.1007/978-981-10-2657-7. arXiv: 1605.09272. Softcover ISBN: 978-981-10-2656-0. eBook ISBN: 978-981-10-2657-7.
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[236] T. Kobayashi, T. Kubo, and M. Pevzner, Classification of differential symmetry breaking operators for differential forms, C. R. Acad. Sci. Paris, Ser.I 354 (2016), 671-676, published online 17 May 2016. DOI: 10.1016/j.crma.2016.04.012.
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[227] T. Kobayashi and M. Pevzner, Differential symmetry breaking operators. II. Rankin-Cohen operators for symmetric pairs, Selecta Mathematica (N.S.) 22 (2016), no. 2, 847-911, Published OnLine 14 December 2015. 65 pages. DOI: 10.1007/s00029-015-0208-8. arXiv:1301.2111. [old title of the preprint version: Rankin-Cohen operators for symmetric pairs].
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[226] T. Kobayashi and M. Pevzner, Differential symmetry breaking operators. I. General theory and F-method., Selecta Mathematica (N.S.) 22 (2016), no. 2, 801-845, Published OnLine 11 December 2015. 45 pages. DOI: 10.1007/s00029-015-0207-9. arXiv:1301.2111. [old title of the preprint version: Rankin-Cohen operators for symmetric pairs].
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[222] T. Kobayashi, A program for branching problems in the representation theory of real reductive groups, Representations of Lie Groups: In Honor of David A. Vogan, Jr. on his 60th Birthday (M. Nevins and P. Trapa, eds.), Progress in Mathematics, vol. 312, Birkhäuser, 2015, pp. 277-322, DOI: 10.1007/978-3-319-23443-4_10. arXiv: 1509.08861. ISBN: 978331923442.
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[219] T. Kobayashi, B. Ørsted, P. Somberg, and V. Souček, Branching laws for Verma modules and applications in parabolic geometry. I, Advances in Mathematics 285, 1796-1852, DOI:10.1016/j.aim.2015.08.020. arXiv:1305.6040.
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[215] T. Kobayashi and G. Savin, Global uniqueness of small representations, Mathematische Zeitschrift 281 (2015), no. 1-2, 215-239. Published online first on 22 May 2015. DOI: 10.1007/s00209-015-1481-0. arXiv: 1412.8019.
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[213] T. Kobayashi and B. Speh, Symmetry breaking for representations of rank one orthogonal groups, vol. 238, Memoirs of American Mathematical Society, no. 1126, 2015, Published electronically May 12, 2015. 118 pp. arXiv: 1310.3213. ISBN: 978-1-4704-1922-6. DOI: 10.1090/memo/1126.
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[209] T. Kobayashi, Analysis on real spherical manifolds and their applications to Shintani functions and symmetry breaking operators, Mathematisches Forschungsinstitut Oberwolfach Report 11 (2014), no. 1, 176-179, Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (organised by B. Krötz, E. M. Opdam, H. Schlichtkrull and P. Trapa, 19-25 January 2014), DOI: 10.4171/OWR/2014/3.
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[204] T. Kobayashi, T. Kubo, and M. Pevzner, Vector-valued covariant differential operators for the Möbius transformation, Lie Theory and Its Applications in Physics (V. Dobrev, ed.), Springer Proceedings in Mathematics & Statistics, vol. 111, 2015, pp. 67-86, arXiv: 1406.0674. DOI: 10.1007/978-4-431-55285-7_6.
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[203] T. Kobayashi, Shintani functions, real spherical manifolds, and symmetry breaking operators, Developments and Retrospectives in Lie Theory Geometric and Analytic Methods (G. Mason, I. Penkov, and Joseph A. Wolf, eds.), Developments in Mathematics, vol. 37, 2014, pp. 127-159, arXiv: 1401.0117. DOI: 10.1007/978-3-319-09934-7_5.
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[201] T. Kobayashi, Symmetric pairs with finite-multiplicity property for branching laws of admissible representations, Proc. Japan Acad., Ser. A, Mathematical Sciences 90 (2014), no. 6, 79-83, DOI: 10.3792/pjaa.90.79.
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[200] T. Kobayashi and T. Matsuki, Classification of finite-multiplicity symmetric pairs, Transformation Groups 19 (2014), 457-493, Special Issue in honour of Professor Dynkin for his 90th birthday. DOI: 10.1007/s00031-014-9265-x. arXiv: 1312.4246.
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[197] T. Kobayashi and B. Speh, Intertwining operators and the restriction of representations of rank one orthogonal groups, C. R. Acad. Sci. Paris, Ser. I 352 (2014), 89-94, DOI: 10.1016/j.crma.2013.11.018. [ full info ]
[196] T. Kobayashi, F-method for symmetry breaking operators, Differential Geometry and its Applications 33 (2014), 272-289, Special Issue ĀgInteraction of Geometry and Representation Theory: Exploring New FrontiersĀh (in honor of Michael Eastwood's 60th birthday). arXiv:1303.3541. DOI:10.1016/j.difgeo.2013.10.003.
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[194] T. Kobayashi, Special functions in minimal representations, Perspectives in Representation Theory in honor of Igor Frenkel on his 60th birthday (Pavel Etingof, Miikhail Khovanov, and Alistair Savage, eds.), Comtemporary Mathematics, vol. 610, Amer. Math. Soc., Providence, RI, 2014, pp. 253-266, DOI: 10.1090/conm/610/12103. arXiv:1301.5505.
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[180] T. Kobayashi, F-method for constructing equivariant differential operators, Geometric Analysis and Integral Geometry (E. T. Quinto, F. B. Gonzalez, and J. Christensen, eds.), Comtemporary Mathematics, vol. 598, Amer. Math. Soc., 2013, pp. 141-148, arXiv: 1212.6862. DOI: 10.1090.conm/598/11998.
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[179] T. Kobayashi, Varna lecture on L2-analysis of minimal representations, Lie Theory and Its Applications in Physics: IXth International Workshop (V. Dobrev, ed.), Springer Proceedings in Mathematics & Statistics, vol. 36, Springer, 2013, pp. 77-93, DOI: 10.1007/978-4-431-54270-4_6. arXiv: 1212.6871.
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[178] T. Kobayashi and Y. Oshima, Classification of symmetric pairs with discretely decomposable restrictions of (g,K)-modules, Journal für die reine und angewandte Mathematik (Crelles Journal) 2015 (2015), no. 703, 201-223, published online 2013 July 13. 19 pp. DOI:10.1515/crelle-2013-0045. arXiv: 1202.5743.
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[177] T. Kobayashi and T. Oshima, Finite multiplicity theorems for induction and restriction, Advances in Mathematics 248 (2013), 921-944. DOI:10.1016/j.aim.2013.07.015. arXiv:1108.3477.
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[176] T. Kobayashi, Propagation of multiplicity-free property for holomorphic vector bundles, Lie Groups: Structure, Actions, and Representations (In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday) (A. Huckleberry, I. Penkov, and G. Zuckerman, eds.), Progress in Mathematics, vol. 306, 2013, pp. 113-140, ISBN: 978-1-4614-7192-9. DOI:10.1007/978-1-4614-7193-6_6. arXiv:math/0607004.
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[165] T. Kobayashi and Y. Oshima, Classification of discretely decomposable Aq(É…) with respect to reductive symmetric pairs, Advances in Mathematics 231 (2012), 2013-2047, arXiv:1104.4400. DOI:10.1016/j.aim.2012.07.006.
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[164] T. Kobayashi, Restrictions of generalized Verma modules to symmetric pairs, Transformation Groups 17 (2012), no. 2, 523-546, (published online first 5 April 2012). DOI: 10.1007/s00031-012-9180-y. arXiv:1008.4544 [math.RT].
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[163] S. Ben Saïd, T. Kobayashi, and B. Ørsted, Laguerre semigroup and Dunkl operators, Compositio Mathematica 148 (2012), 1265-1336, DOI: 10.1112/S0010437X11007445. arXiv:0907.3749 [math.RT].
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[154] T. Kobayashi, Branching problems of Zuckerman derived functor modules, Representation Theory and Mathematical Physics (in honor of Gregg Zuckerman) (Jeffrey Adams, Bong Lian, and Siddhartha Sahi, eds.), Contemporary Mathematics, vol. 557, Amer. Math. Soc., Providence, RI, 2011, pp. 23-40, ISBNĀF 9780821852460, arXiv:1104.4399.
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[151] T. Kobayashi, B. Ørsted, and M. Pevzner, Geometric analysis on small unitary representations of GL(n,R), J. Funct. Anal. 260 (2011), no. 6, 1682-1720, (published online first, on 28 December 2010). DOI: 10.1016/j.jfa/2010.12.008. arXiv:1002.3006 [math.RT].
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[147] J.-L. Clerc, T. Kobayashi, B. Ørsted, and M. Pevzner, Generalized Bernstein-Reznikov integrals, Mathematische Annalen 349 (2011), no. 2, 395-431, (published online first, on 4 May 2010). DOI: 10.1007/s00208-010-0516-4. arXiv:0906.2874 [math.CA].
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[126] T. Kobayashi, Hidden symmetries and spectrum of the Laplacian on an indefinite Riemannian manifold, Spectral Analysis in Geometry and Number Theory (in honor of Professor Sunada) (M. Kotani, H. Naito, and T. Tate, eds.), Contemp. Math., vol. 484, Amer. Math. Soc., Providence, RI, 2009, pp. 73-87.
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[101] T. Kobayashi, Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs, Representation Theory and Automorphic Forms, Progr. Math., vol. 255, Birkhäuser, 2007, pp. 45-109, math.RT/0607002.
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[87] T. Kobayashi, Theory of discrete decomposable branching laws of unitary representations of semisimple Lie groups and some applications, Sugaku Expositions 18 (2005), 1-37, a translation of the original article in Japanese.
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[85] T. Kobayashi, Restrictions of unitary representations of real reductive groups, Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces (J.-P. Anker and B. Ørsted, eds.), Progress in Mathematics 229, Birkhauser, 2005, pp. 139-207.
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[65] T. Kobayashi, Branching problems of unitary representations, Proc. of ICM 2002, Beijing, vol. 2, 2002, pp. 615-627, math.RT/0304326.
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[60] T. Kobayashi, Discretely decomposable restrictions of unitary representations of reductive Lie groups - examples and conjectures, Advanced Study in Pure Mathematics, Analysis on Homogeneous Spaces and Representation Theory of Lie Groups, Okayama-Kyoto (T. Kobayashi, M. Kashiwara, T. Matsuki, K. Nishiyama, and T. Oshima, eds.), vol. 26, 2000, pp. 98-126.
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[59] T. Kobayashi, Multiplicity-free restrictions of unitary highest weight modules for reductive symmetric pairs, preprint UTMS 2000-1.
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[54] T. Kobayashi, Theory of discretely decomposable restrictions of unitary representations of semisimple Lie groups and its developments, Sugaku 51 (1999), no. 4, 337-356 (in Japanese), an English translation is available.
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[53] T. Kobayashi, Theory of discretely decomposable restrictions of unitary representations and its development, Proceedings of Plenary Lectures of the Mathematical Society of Japan, held at Gakushuin University, Tokyo, March, 1999, 1999, pp. 1-19 (in Japanese).
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[50] T. Kobayashi, Discrete decomposability of the restriction of Aq(É…) with respect to reductive subgroups III - restriction of Harish-Chandra modules and associated varieties, Invent. Math. 131 (1998), 229-256.
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[49] T. Kobayashi and T. Oda, A vanishing theorem for modular symbols on locally symmetric spaces, Comment. Math. Helv. 73 (1998), 45-70.
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[48] T. Kobayashi, Discrete decomposability of the restriction of Aq(É…) with respect to reductive subgroups II - micro-local analysis and asymptotic K-support, Annals of Math. 147 (1998), no. 3, 709-729.
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[47] T. Kobayashi, Discrete series representations for the orbit spaces arising from two involutions of real reductive Lie groups, J. Funct. Anal. 152 (1998), 100-135.
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[46] T. Kobayashi, Harmonic analysis on homogeneous manifolds of reductive type and unitary representation theory, Translations, Series II, Selected Papers on Harmonic Analysis, Groups, and Invariants (K. Nomizu, ed.), vol. 183, Amer. Math. Soc., 1998, pp. 1-31, ISBN 0-8218-0840-0.
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[42] T. Kobayashi, Lp-analysis on homogeneous manifolds of reductive type and representation theory, Proc. Japan Acad. 73 (1997), 62-66.
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[40] T. Kobayashi, Monastir Seminar on the restriction of unitary representations and their applications, Proceedings of the CIMPA School, held in Tunisia, July-August 1996 (P. Torasso, ed.), 1997.
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[39] T. Kobayashi, On the restriction of unitary representations and their applications, Proceedings of Symposium on Representation Theory, Mikawa, 1996, pp. 131-141 (in Japanese).
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[38] T. Kobayashi and T. Oshima, Multiplicities of induced representations of semisimple Lie groups, unpublished notes, 1996.
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[37] T. Kobayashi, A vanishing theorem of modular symbols on locally symmetric varieties, (notes taken by S. Ishikawa), Proceedings of Representation Theory and Related Topics, Kurashiki 1996 (N. Shimeno, ed.), 1996, pp. 1-16 (in Japanese).
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[34] T. Kobayashi, Introduction to harmonic analysis on spherical homogeneous spaces, Proceedings of 3rd Summer School on Number Theory ''Homogeneous Spaces and Automorphic Forms'' held at Rikkyo University, January 1995 and at Yamagata-mura in Nagano August 1995 (F. Sato, ed.), 1995, pp. 22-41 (in Japanese).
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[33] T. Kobayashi, The restriction of Aq(É…) to reductive subgroups II, Proc. Japan Acad. Ser. A 71 (1995), 24-26.
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[30] T. Kobayashi, Discrete decomposability of the restriction of Aq(É…) with respect to reductive subgroups and its applications, Invent. Math. 117 (1994), 181-205.
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[25] T. Kobayashi, The restriction of Aq(É…) to reductive subgroups, Proc. Japan Acad. Ser. A 69 (1993), 262-267.
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[18] T. Kobayashi, Some examples of the branching rule of unitary representations associated to isomorphisms of homogeneous spaces, unpublished notes, 1990.
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Updated: 26 October 2019

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