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https://hdl.handle.net/2440/126584
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Type: | Journal article |
Title: | A geometric realisation of tempered representations restricted to maximal compact subgroups |
Author: | Hochs, P. Song, Y. Yu, S. |
Citation: | Mathematische Annalen, 2020; 378(1-2):97-152 |
Publisher: | Springer-Verlag |
Issue Date: | 2020 |
ISSN: | 0025-5831 1432-1807 |
Statement of Responsibility: | Peter Hochs, Yanli Song and Shilin Yu |
Abstract: | Let G be a connected, linear, real reductive Lie group with compact centre. Let K<G be maximal compact. For a tempered representation π of G, we realise the restriction π|K as the K-equivariant index of a Dirac operator on a homogeneous space of the form G/H, for a Cartan subgroup H<G. (The result in fact applies to every standard representation.) Such a space can be identified with a coadjoint orbit of G, so that we obtain an explicit version of Kirillov’s orbit method for π|K. In a companion paper, we use this realisation of π|K to give a geometric expression for the multiplicities of the K-types of π, in the spirit of the quantisation commutes with reduction principle. This generalises work by Paradan for the discrete series to arbitrary tempered representations. |
Description: | Published: 16 May 2020 |
Rights: | © Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
DOI: | 10.1007/s00208-020-02006-4 |
Published version: | http://dx.doi.org/10.1007/s00208-020-02006-4 |
Appears in Collections: | Aurora harvest 8 Mathematical Sciences publications |
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