Gradings of positive rank on simple Lie algebras

被引：0
作者：
Mark Reeder
Paul Levy
Jiu-Kang Yu
Benedict H. Gross
机构：
[1] Boston College,Department of Mathematics
[2] Lancaster University,Department of Mathematics and Statistics
[3] Purdue University,Department of Mathematics
[4] Harvard University,Department of Mathematics
来源：
Transformation Groups | 2012年 / 17卷
关键词：
Conjugacy Class; Weyl Group; Maximal Torus; Cartan Subalgebra; Levi Subgroup;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We complete the classification of positive rank gradings on Lie algebras of simple algebraic groups over an algebraically closed field k whose characteristic is zero or not too small, and we determine the little Weyl groups in each case. We also classify the stable gradings and prove Popov’s conjecture on the existence of a Kostant section.
引用
收藏
页码：1123 / 1190
页数：67
相关论文
共 29 条
  • [1] Carter R(1972)Conjugacy classes in the Weyl group Compositio Math. 25 1-59
  • [2] de Graaf W(2011)Computing representatives of nilpotent orbits of J. Symb. Comput. 46 438-458
  • [3] de Graaf W(2012)-groups Algebr. Represent. Theory 15 613-638
  • [4] Yakimova O(2010)Good index behaviour of θ-representations, I Duke Math. J. 154 431-508
  • [5] Gross B(1988)Arithmetic invariants of discrete Langlands parameters Israel J. Math. 62 129-168
  • [6] Reeder M(1959)Fixed point varieties on affine flag manifolds Amer. J. Math. 81 973-1032
  • [7] Kazhdan D(1971)The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group Amer. J. Math. 93 753-809
  • [8] Lusztig G(2009)Orbits and representations associated with symmetric spaces Contemp. Math. 478 99-101
  • [9] Kostant B(2007)Characters of simplylaced nonconnected groups verus characters of nonsimplylaced connected groups Adv. Math. 210 505-559
  • [10] Kostant B(2009)Involutions of reductive Lie algebras in positive characteristic Transform. Groups 14 417-461
123