ENHANCED ADJOINT ACTIONS AND THEIR ORBITS FOR THE GENERAL LINEAR GROUP

被引：0

作者：

Nishiyama, Kyo ^{[1
]}

Ohta, Takuya ^{[2
]}

机构：

[1] Aoyama Gakuin Univ, Dept Phys & Math, Sagamihara, Kanagawa, Japan

[2] Tokyo Denki Univ, Dept Math, Adachi Ku, Tokyo, Japan

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2019年 / 298卷 / 01期

关键词：

enhanced nilpotent cone; exotic nilpotent cone; adjoint quotient; classical invariant theory; REPRESENTATIONS; CLOSURES;

D O I：

10.2140/pjm.2019.298.141

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study an enhanced adjoint action of the general linear group on a product of its Lie algebra and a vector space consisting of several copies of defining representations and its duals. We determine regular semisimple orbits (i.e., closed orbits of maximal dimension) and the structure of enhanced null cone, including its irreducible components and their dimensions.

引用

页码：141 / 155

页数：15

共 50 条

[41] Primitive vectors in induced supermodules for general linear supergroups [J].

Marko, Frantisek .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2015, 219 (04) :978-1007

[42] Algebraic isomonodromic deformations of logarithmic connections on the Riemann sphere and finite braid group orbits on character varieties [J].

Cousin, Gael .

MATHEMATISCHE ANNALEN, 2017, 367 (3-4) :965-1005

[43] Super tableaux and a branching rule for the general linear Lie superalgebra [J].

Clark, Sean ;

Peng, Yung-Ning ;

Thamrongpairoj, S. Kuang .

LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (02) :274-282

[44] The abelian subalgebras of maximal dimensions for general linear Lie superalgebras [J].

Wang, Shujuan ;

Liu, Andwende .

LINEAR & MULTILINEAR ALGEBRA, 2016, 64 (10) :2081-2089

[45] Homotopy coherent mapping class group actions and excision for Hochschild complexes of modular categories [J].

Schweigert, Christoph ;

Woike, Lukas .

ADVANCES IN MATHEMATICS, 2021, 386

[46] Structure Group and Fermion-Mass-Term in General Nonlocality [J].

Han, Lei ;

Wang, Hai-Jun .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2016, 55 (01) :577-594

[47] Lie theory for asymptotic symmetries in general relativity: The BMS group [J].

Prinz, David ;

Schmeding, Alexander .

CLASSICAL AND QUANTUM GRAVITY, 2022, 39 (06)

[48] Linear and Shalika local periods for the mirabolic group, and some consequences [J].

Matringe, Nadir .

JOURNAL OF NUMBER THEORY, 2014, 138 :1-19

[49] SYMMETRIES OF NON-LINEAR SYSTEMS: GROUP APPROACH TO THEIR QUANTIZATION [J].

Aldaya, V. ;

Calixto, M. ;

Guerrero, J. ;

Lopez-Ruiz, F. F. .

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2011, 8 (06) :1329-1354

[50] Generalized Bump-Hoffstein conjecture for coverings of the general linear groups [J].

Gao, Fan .

JOURNAL OF ALGEBRA, 2018, 499 :183-228

← 1 2 3 4 5 →