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
收藏
页码：141 / 155
页数：15
相关论文
共 50 条
  • [1] Sernigroup Actions on Adjoint Orbits
    do Rocio, Osvaldo G.
    San Martin, Luiz A. B.
    Verdi, Marcos A.
    JOURNAL OF LIE THEORY, 2012, 22 (04) : 931 - 948
  • [2] Group actions and orbits
    Isaacs, I. M.
    ARCHIV DER MATHEMATIK, 2012, 98 (05) : 399 - 401
  • [3] Group actions and orbits
    I. M. Isaacs
    Archiv der Mathematik, 2012, 98 : 399 - 401
  • [4] Linear group actions with at most three orbits of the largest size
    Burcu Çınarcı
    Thomas Michael Keller
    Monatshefte für Mathematik, 2024, 203 : 313 - 322
  • [5] Linear group actions with at most three orbits of the largest size
    Cinarci, Burcu
    Keller, Thomas Michael
    MONATSHEFTE FUR MATHEMATIK, 2024, 203 (02): : 313 - 322
  • [6] Adjoint and coadjoint orbits of the Poincare group
    Cushman, Richard
    van der Kallen, Wilberd
    ACTA APPLICANDAE MATHEMATICAE, 2006, 90 (1-2) : 65 - 89
  • [7] Adjoint and Coadjoint Orbits of the Poincaré Group
    Richard Cushman
    Wilberd van der Kallen
    Acta Applicandae Mathematica, 2006, 90 : 65 - 89
  • [8] Dentistry of orbits of linear group actions and equidistribution properties of random walks
    Conze, JP
    Guivarc'h, YG
    RIGIDITY IN DYNAMICS AND GEOMETRY: CONTRIBUTIONS FROM THE PROGRAMME ERGODIC THEORY, GEOMETRIC RIGIDITY AND NUMBER THEORY, 2002, : 39 - 76
  • [9] Orbits of actions of group superschemes
    Bovdi, V. A.
    Zubkov, A. N.
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2023, 227 (11)
  • [10] Real adjoint orbits of special linear groups
    Gongopadhyay, Krishnendu
    Lohan, Tejbir
    Maity, Chandan
    ILLINOIS JOURNAL OF MATHEMATICS, 2024, 68 (03)
12345