Scattered Representations of Complex Classical Lie Groups

被引：3

作者：

Dong, Chao-Ping ^{[1
]}

Wong, Kayue Daniel ^{[2
]}

机构：

[1] Soochow Univ, Sch Math Sci, Suzhou 215006, Peoples R China

[2] Chinese Univ Hong Kong, Sch Sci & Engn, Shenzhen 518172, Guangdong, Peoples R China

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 14期

基金：

中国国家自然科学基金;

关键词：

DIRAC COHOMOLOGY; UNITARY REPRESENTATIONS;

D O I：

10.1093/imrn/rnaa388

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

As a continuation of [9], this paper studies scattered representations of SO(2n+1, C), Sp(2n, C), and SO(2n, C). We describe the Zhelobenko parameters of these representations, count their cardinality, and determine their spin-lowest K-types. We also disprove a conjecture raised in 2015 asserting that the unitary dual can be obtained via parabolic induction from irreducible unitary representations with nonzero Dirac cohomology.

引用

页码：10431 / 10457

页数：27

共 50 条

[41] COMPLEX REPRESENTATIONS OF SOME CLASSICAL GROUPS OVER A FINITE-FIELD
NAGORNYI, SV
DOKLADY AKADEMII NAUK SSSR, 1978, 243 (06): : 1391 - 1393
[42] On the existence of homomorphisms between principal series representations of complex semisimple Lie groups
Abe, Noriyuki
JOURNAL OF ALGEBRA, 2011, 330 (01) : 468 - 481
[43] INTRODUCTION TO LIE-GROUPS AND THEIR REPRESENTATIONS
GUICHARDET, A
LECTURE NOTES IN MATHEMATICS, 1982, 948 : 131 - 163
[44] ON THE DECOMPOSITION OF UNITARY REPRESENTATIONS OF LIE GROUPS
MAUTNER, FI
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 2 (03) : 490 - 496
[45] Quaternionic representations of exceptional Lie groups
Loke, HY
PACIFIC JOURNAL OF MATHEMATICS, 2003, 211 (02) : 341 - 367
[46] INDUCED REPRESENTATIONS OF NILPOTENT LIE GROUPS
KIRILLOV, AA
DOKLADY AKADEMII NAUK SSSR, 1959, 128 (05): : 886 - 889
[47] REAL ANALYTIC ACTIONS OF COMPLEX SYMPLECTIC GROUPS AND OTHER CLASSICAL LIE-GROUPS ON SPHERES
UCHIDA, F
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1986, 38 (04) : 661 - 677
[48] On modular Lie representations of finite groups
Bryant, R. M.
Stohr, Ralph
TURKISH JOURNAL OF MATHEMATICS, 2007, 31 : 25 - 43
[49] COCYCLE REPRESENTATIONS OF SOLVABLE LIE GROUPS
MOSCOVICI, H
VERONA, A
MATHEMATISCHE ZEITSCHRIFT, 1978, 160 (02) : 183 - 194
[50] UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
KIRILLOV, AA
DOKLADY AKADEMII NAUK SSSR, 1960, 130 (05): : 966 - 968

← 1 2 3 4 5 →