T. Kobayashi, Global analysis by hidden symmetry, Representation Theory, Number Theory, and Invariant Theory: In Honor of Roger Howe on the Occasion of His 70th Birthday (Jim Cogdell, Ju-Lee Kim, and Chen-Bo Zhu, eds.), Progress in Mathematics, vol. 323 (2017), pp. 359-397. DOI: 10.1007/978-3-319-59728-7_13. arXiv: 160808356. ISBN 978-3-319-59727-0..

Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects:

(A) global analysis on X by using representations of G (hidden symmetry);

(B) global analysis on X by using representations of G';

(C) branching laws of representations of G when restricted to the subgroup G'.

We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting when XC is G'C-spherical. Applications to branching problems of unitary representations, and to spectral analysis on pseudo-Riemannian locally symmetric spaces are also discussed.

[ DOI |  arXiv | full pdf | preprint version(pdf) ]

Home EnHome Jp

© Toshiyuki Kobayashi