RESTRICTION OF IRREDUCIBLE UNITARY REPRESENTATIONS OF Spin(N, 1) TO PARABOLIC SUBGROUPS

被引：0

作者：

Liu, Gang ^{[1
]}

Oshima, Yoshiki ^{[2
]}

Yu, Jun ^{[3
,4
]}

机构：

[1] Univ Lorraine, Inst Elie Cartan Lorraine, CNRS UMR 7502, 3 Rue Augustin Fresnel, F-57045 Metz, France

[2] Univ Tokyo, Grad Sch Math Sci, 3-8-1,Komaba,Meguro Ku, Tokyo 1538914, Japan

[3] Peking Univ, Beijing Int Ctr Math Res, 5 Yiheyuan Rd, Beijing 100871, Peoples R China

[4] Peking Univ, Sch Math Sci, 5 Yiheyuan Rd, Beijing 100871, Peoples R China

来源：

REPRESENTATION THEORY | 2023年 / 27卷

关键词：

Unitary representation; branching law; discrete series; Fourier trans-form; moment map; coadjoint orbit; orbit method; HARISH-CHANDRA MODULES; BRANCHING LAWS; DISCRETE DECOMPOSABILITY; REDUCTIVE SUBGROUPS; TENSOR-PRODUCTS; RESPECT; MULTIPLICITIES; A(Q)(LAMBDA); QUANTIZATION; ORBITS;

D O I：

10.1090/ert/658

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we obtain explicit branching laws for all irreducible unitary representations of G = Spin(N, 1) when restricted to a parabolic sub-group P. The restriction turns out to be a finite direct sum of irreducible unitary representations of P. We also verify Duflo's conjecture for the branching laws of discrete series representations of G with respect to P. That is to show: in the framework of the orbit method, the branching law of a discrete series representation is determined by some geometric behavior of the moment map for the corresponding coadjoint orbit.

引用

页码：887 / 932

页数：46

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