Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups O(p, q)

被引：2

作者：

Kobayashi, Toshiyuki ^{[1
]}

Leontiev, Alex ^{[2
]}

机构：

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

[2] Univ Tokyo, Kavli Inst Phys & Math Universe, 5-1-5 Kashiwanoha, Kashiwa, Chiba 2778583, Japan

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2017年 / 93卷 / 08期

关键词：

Representation theory; reductive group; branching law; broken symmetry; conformal geometry; symmetry breaking operator; DISCRETE DECOMPOSABILITY; REDUCTIVE SUBGROUPS; A(Q)(LAMBDA); RESPECT; MODULES;

D O I：

10.3792/pjaa.93.86

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For the pair (G, G '') = (O(p + 1, q + 1), 0(p, q + 1)), we construct and give a complete classification of intertwining operators (symmetry breaking operators) between most degenerate spherical principal series representations of G and those of the subgroup G', extending the work initiated by Kobayashi and Speh [Mem. Amer. Math. Soc. 2015] in the real rank one case where q = 0. Functional identities and residue formula of the regular symmetry breaking operators are also provided explicitly. The results contribute to Program C of branching problems suggested by the first author [Progr. Math. 2015].

引用

页码：86 / 91

页数：6

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