Irreducible representations of semisimple algebraic groups and supersolvable lattices

被引：1

作者：

Can, Mahir Bilen ^{[1
]}

机构：

[1] Tulane Univ, New Orleans, LA 70118 USA

来源：

JOURNAL OF ALGEBRA | 2012年 / 351卷 / 01期

关键词：

Irreducible representations of semisimple groups; J-irreducible monoids; Cross section lattices; Supersolvable lattices; Characteristic polynomials; Mobius functions; SHELLABILITY; MONOIDS; CLASSIFICATION; POSETS;

D O I：

10.1016/j.jalgebra.2011.11.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Lambda be the cross section lattice of an irreducible representation of a semisimple algebraic group. Certain combinatorial properties of Lambda are studied. Supersolvable Lambda'S are determined in terms of Dynkin diagrams. The characteristic polynomial of a supersolvable Lambda is computed. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：235 / 250

页数：16

共 50 条

[1] COMPUTING IRREDUCIBLE REPRESENTATIONS OF SUPERSOLVABLE GROUPS
BAUM, U
CLAUSEN, M
[J]. MATHEMATICS OF COMPUTATION, 1994, 63 (207) : 351 - 359
[2] ALMOST CYCLIC REGULAR SEMISIMPLE ELEMENTS IN IRREDUCIBLE REPRESENTATIONS OF SIMPLE ALGEBRAIC GROUPS
D. M. TESTERMAN
ALEXANDRE E. ZALESSKI
[J]. Transformation Groups, 2023, 28 : 1299 - 1324
[3] ALMOST CYCLIC REGULAR SEMISIMPLE ELEMENTS IN IRREDUCIBLE REPRESENTATIONS OF SIMPLE ALGEBRAIC GROUPS
Testerman, D. M.
Zalesski, A. L. E. X. A. N. D. R. E. E. E.
[J]. TRANSFORMATION GROUPS, 2023, 28 (3) : 1299 - 1324
[4] CLASSIFICATION OF IRREDUCIBLE TEMPERED REPRESENTATIONS OF SEMISIMPLE GROUPS
KNAPP, AW
ZUCKERMAN, GJ
[J]. ANNALS OF MATHEMATICS, 1982, 116 (02) : 389 - 455
[5] CLASSIFICATION OF IRREDUCIBLE REPRESENTATIONS OF SEMISIMPLE LIE GROUPS
VOGAN, DA
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1977, 74 (07) : 2649 - 2650
[6] Representations of semisimple lattices in mapping class groups
Yeung, SK
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2003, 2003 (31) : 1677 - 1686
[7] CONJUGACY CLASSES OF SEMISIMPLE ELEMENTS, AND IRREDUCIBLE REPRESENTATIONS OF ALGEBRAIC MONOIDS
RENNER, LE
[J]. COMMUNICATIONS IN ALGEBRA, 1988, 16 (09) : 1933 - 1943
[8] ON RESTRICTIONS OF IRREDUCIBLE MODULAR-REPRESENTATIONS OF SEMISIMPLE ALGEBRAIC-GROUPS AND SYMMETRICAL GROUPS TO SOME NATURAL SUBGROUPS
KLESHCHEV, AS
[J]. DOKLADY AKADEMII NAUK, 1993, 333 (01) : 11 - 12
[9] Survey of irreducible unitary representations of semisimple Lie groups
Knapp, AW
[J]. GROUP 21 - PHYSICAL APPLICATIONS AND MATHEMATICAL ASPECTS OF GEOMETRY, GROUPS, AND ALGEBRA, VOLS 1 AND 2, 1997, : 89 - 98
[10] CLASSIFICATION OF IRREDUCIBLE TEMPERED REPRESENTATIONS OF SEMISIMPLE LIE GROUPS
KNAPP, AW
ZUCKERMAN, G
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1976, 73 (07) : 2178 - 2180

← 1 2 3 4 5 →