SUBGROUPS OF SIMPLE ALGEBRAIC GROUPS CONTAINING REGULAR TORI, AND IRREDUCIBLE REPRESENTATIONS WITH MULTIPLICITY 1 NON-ZERO WEIGHTS

被引：7

作者：

Testerman, D. M. ^{[1
]}

Zalesski, A. E. ^{[2
]}

机构：

[1] Ecole Polytech Fed Lausanne, FSP MATHGEOM, Stn 8, CH-1015 Lausanne, Switzerland

[2] Acad Sci Belarus, Dept Phys Math & Informat, Minsk 220000, BELARUS

来源：

TRANSFORMATION GROUPS | 2015年 / 20卷 / 03期

关键词：

LONG ROOT ELEMENTS; EXCEPTIONAL GROUPS; MODULES; FIELDS;

D O I：

10.1007/s00031-015-9321-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple linear algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of independent interest. In particular, we determine the irreducible representations of simple algebraic groups whose non-zero weights occur with multiplicity 1.

引用

页码：831 / 861

页数：31

共 9 条

[1] SUBGROUPS OF SIMPLE ALGEBRAIC GROUPS CONTAINING REGULAR TORI, AND IRREDUCIBLE REPRESENTATIONS WITH MULTIPLICITY 1 NON-ZERO WEIGHTS
D. M. TESTERMAN
A. E. ZALESSKI
[J]. Transformation Groups, 2015, 20 : 831 - 861
[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] Weight zero in tensor-decomposable irreducible representations of simple algebraic groups
Baranov, Alexander
Zalesski, Alexandre
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2021, 225 (12)
[5] Restrictions of irreducible representations of classical algebraic groups to root A1-subgroups
Osinovskaya, AA
[J]. COMMUNICATIONS IN ALGEBRA, 2003, 31 (05) : 2357 - 2379
[6] IRREDUCIBLE REPRESENTATIONS OF SIMPLE ALGEBRAIC-GROUPS CONTAINING MATRICES WITH BIG JORDAN BLOCKS
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[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1995, 71 : 281 - 332
[7] On multiplicity 1 eigenvalues of elements in irreducible representations of finite quasi-simple groups
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Zalesski, A. E.
[J]. JOURNAL OF GROUP THEORY, 2007, 10 (05) : 585 - 612
[8] ON RESTRICTIONS OF IRREDUCIBLE MODULAR-REPRESENTATIONS OF SEMISIMPLE ALGEBRAIC-GROUPS AND SYMMETRICAL GROUPS TO SOME NATURAL SUBGROUPS .1.
KLESHCHEV, AS
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1994, 69 : 515 - 540
[9] Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block
Testerman, Donna M.
Zalesski, Alexandre E.
[J]. JOURNAL OF GROUP THEORY, 2018, 21 (01) : 1 - 20

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