Analysis on minimal representations

[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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[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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[196] T. Kobayashi, F-method for symmetry breaking operators, Differential Geometry and its Applications 33 (2014), 272-289, Special Issue gInteraction of Geometry and Representation Theory: Exploring New Frontiersh (in honor of Michael Eastwood's 60th birthday). arXiv:1303.3541. DOI:10.1016/j.difgeo.2013.10.003.
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[195] J. Hilgert, T. Kobayashi, and J. Möllers, Minimal representations via Bessel operators, J. Math. Soc. Japan 66 (2014), 349-414, DOI: 10.2969/jmsj/06620349. arXiv:1106.3621.
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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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[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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[166] J. Hilgert, T. Kobayashi, J. Möllers, and B. Ørsted, Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups, Journal of Functional Analysis 263 (2012), 3492-3563. DOI: 10.1016/j.jfa.2012.08.026. arXiv:1203.5462.
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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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[157] T. Kobayashi, Geometric analysis on minimal representations, Ninth Oka Symposium Lecture Notes (J. Matsuzawa and S. Tsunoda, eds.), Department of Mathematics, Faculty of Science, Nara Women's University, 2011, pp. 27-61.
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[152] T. Kobayashi and J. Möllers, An integral formula for L2-eigenfunctions of a fourth order Bessel-type differential operator, Integral Transforms and Special Functions 22 (2011), no. 7, 521-531, (published online first, on 27 January 2011), DOI: 10.1080/10652469.2010.533270. arXiv:1003.2699 [math.CA].
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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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[150] T. Kobayashi, Algebraic analysis of minimal representations, Publ. RIMS (Publications of the Research Institute for Mathematical Sciences) 47, no. 2, Special issue in commemoration of the golden jubilee of algebraic analysis, (2011), 585-611. arXiv:1001.0224 [math.RT].
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[149] J. Hilgert, T. Kobayashi, G. Mano, and J. Möllers, Orthogonal polynomials associated to a certain fourth order differential equation, Ramanujan Journal 26 (2011), 295-310, DOI: 10.1007/s11139-011-9338-6. arXiv:0907.2612 [math.CA].
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[148] J. Hilgert, T. Kobayashi, G. Mano, and J. Möllers, Special functions associated to a certain fourth order differential equation, Ramanujan Journal 26 (2011), no.1, 1-34. (published online August 31, 2011). DOI: 10.1007/s11139-011-9315-0. arXiv:0907.2608 [math.CA].
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[146] T. Kobayashi and G. Mano, The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p, q), Mem. Amer. Math. Soc. 212, no. 1000, vi+132 pp., (published online first, on 4 February 2011). DOI: 10.1090/S0065-9266-2011-00592-7. arXiv:0712.1769 [math.RT].
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[132] S. Ben Saïd, T. Kobayashi, and B. Ørsted, Generalized Fourier transforms Fk,a, C. R. Math. Acad. Sci. Paris 347 (2009), 1119-1124, (published online first, on 21 August 2009).
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[106] T. Kobayashi and G. Mano, Integral formula of the unitary inversion operator for the minimal representation of O(p,q), Proc. Japan Acad. Ser. A 83 (2007), no. 3, 27-31.
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[105] T. Kobayashi and G. Mano, The inversion formula and holomorphic extension of the minimal representation of the conformal group, Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory: In Honour of Roger E. Howe (Jian-Shu Li, Eng-Chye Tan, Nolan Wallach, and Chen-Bo Zhu, eds.), Singapore University Press and World Scientific Publishing, 2007, pp. 159-223. ISBN 978-9812770783. math.RT/0607007.
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[94] T. Kobayashi and G. Mano, The inversion operator for the minimal representation of O(p,q), Surikaiseki Kokyuroku, RIMS 1467 (2006), 51-61 (in Japanese), Representation Theory of Groups and Extension of Harmonic Analysis (edited by T. Kawazoe).
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[91] T. Kobayashi, Fourier transform of a minimal K-type vector in the minimal representation of O(p+1,q+1), Surikaiseki Kokyuroku, RIMS 1421 (2005), 1-11 (in Japanese), Automorphic Forms on Sp(2,R) and SU(2,2), III (organized by T. Oda).
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[90] T. Kobayashi and G. Mano, The minimal representation of O(p,2) and an integral formula for the inversion operator, Surikaiseki Kokyuroku, RIMS 1410 (2005), 173-187 (in Japanese), Representation Theory and Harmonic Analysis on Homogeneous Spaces (organized by J. Inoue).
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[83] T. Kobayashi and G. Mano, Integral formulas for the minimal representations for O(p, 2), Acta Appl. Math. 83 (2005), 103-113.
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[77] T. Kobayashi, Schrodinger model of the minimal representation of O(p,q), Surikaiseki Kokyuroku, RIMS 1342 (2003), 107-116 (in Japanese), Automorphic Forms on Type IV Symmetric Domains (edited by T. Oda).
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[75] T. Kobayashi, Conformal geometry and global solutions to the Yamabe equations on classical pseudo-riemannian manifolds, Supplemento di Rendiconti del Circolo Matematico di Palermo, Serie II 71 (2003), 15-40, Lecture Notes of the 22th Winter School 2002 on Geometry and Physics, Czech Republic.
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[74] T. Kobayashi and B. Ørsted, Analysis on the minimal representations of O(p,q), III. - Ultra-hyperbolic equations on Rp-1,q-1, Adv. Math. 180 (2003), 551-595. math.RT/0111086
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[73] T. Kobayashi and B. Ørsted, Analysis on the minimal representations of O(p,q), II. - Branching laws, Adv. Math. 180 (2003), 513-550. math.RT/0111085
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[72] T. Kobayashi and B. Ørsted, Analysis on the minimal representations of O(p,q), I. - Realization and conformal geometry, Adv. Math. 180 (2003), 486-512. math.RT/0111083
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[70] T. Kobayashi, The canonical inner product on the space of solutions of the Yamabe operator, Surikaiseki Kokyuroku, RIMS 1294 (2002), 76-86 (in Japanese), Representations of Noncomutative Algebraic Systems and Harmonic Analysis (organized by T. Ohta).
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[69] T. Kobayashi, On the canonical inner product on the space of global solutions of the Yamabe operator, Proceedings of Differential Geometry Symposium on ''Various Geometric Structures'', 2002, pp. 4-5.
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[51] T. Kobayashi and B. Ørsted, Conformal geometry and branching laws for unitary representations attached to minimal nilpotent orbits, C. R. Acad. Sci. Paris 326 (1998), 925-930.
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Updated: 26 October 2019

© Toshiyuki Kobayashi