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

[31] RELATIVE LIE-ALGEBRA CO-HOMOLOGY AND UNITARY REPRESENTATIONS OF COMPLEX LIE GROUPS
ENRIGHT, TJ
DUKE MATHEMATICAL JOURNAL, 1979, 46 (03) : 513 - 525
[32] Arcs of representations of knot groups into Lie groups
Ben Abdelghani, L
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 327 (11): : 933 - 937
[33] On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups
Babich M.V.
Journal of Mathematical Sciences, 2015, 209 (6) : 830 - 844
[34] Linking Lie groupoid representations and representations of infinite-dimensional Lie groups
Habib Amiri
Alexander Schmeding
Annals of Global Analysis and Geometry, 2019, 55 : 749 - 775
[35] Lie Groups, Lie Algebras, and Representations (An Elementary Introduction)
Kurusa, Arpad
ACTA SCIENTIARUM MATHEMATICARUM, 2007, 73 (1-2): : 424 - 425
[36] Lie groups, Lie algebras, and representations: An elementary introduction
Hunacek, Mark
MATHEMATICAL GAZETTE, 2005, 89 (514): : 149 - +
[37] Linking Lie groupoid representations and representations of infinite-dimensional Lie groups
Amiri, Habib
Schmeding, Alexander
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2019, 55 (04) : 749 - 775
[38] Representations of Lie algebras from representations of quantum groups
Moylan, P
CZECHOSLOVAK JOURNAL OF PHYSICS, 1998, 48 (11) : 1457 - 1464
[39] Holomorphic highest weight representations of infinite dimensional complex classical groups
Neeb, KH
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1998, 497 : 171 - 222
[40] Unipotent elements of finite groups of Lie type and realization fields of their complex representations
Tiep, PH
Zalesskii, AE
JOURNAL OF ALGEBRA, 2004, 271 (01) : 327 - 390

← 1 2 3 4 5 →