Abelian ideals of a Sorel subalgebra and root systems

被引:7
作者
Panyushev, Dmitri I. [1 ,2 ]
机构
[1] Independent Univ Moscow, Moscow 119002, Russia
[2] RAS, Inst Informat Transmiss Problems, Moscow 127994, Russia
关键词
Root system; Borel subalgebra; minuscule element; abelian ideal; AD-NILPOTENT IDEALS; BOREL SUBALGEBRA;
D O I
10.4171/JEMS/496
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let g be a simple Lie algebra and 216 degrees the poset of non-trivial abelian ideals of a fixed Borel subalgebra of g. In [8], we constructed a partition 216 degrees = Li-mu 216 mu parameterised by the long positive roots of g and studied the subposets 216(mu). In this note, we show that this partition is compatible with intersections, relate it to the Kostant Peterson parameterisation and to the centralisers of abelian ideals. We also prove that the poset of positive roots of g is a join-semilattice.
引用
收藏
页码:2693 / 2708
页数:16
相关论文
共 15 条
  • [1] BOURBAKI N, 1968, GROUPES ALGEBRES LIE, pCH4
  • [2] Abelian ideals of Borel subalgebras and affine Weyl groups[J]. Cellini, P;Papi, P. ADVANCES IN MATHEMATICS, 2004(02)
  • [3] ad-nilpotent ideals of a Borel subalgebra[J]. Cellini, P;Papi, P. JOURNAL OF ALGEBRA, 2000(01)
  • [4] Ad-nilpotent ideals of a Borel subalgebra II[J]. Cellini, P;Papi, P. JOURNAL OF ALGEBRA, 2002(01)
  • [5] Humphreys J.E., 1992, REFLECTION GROUPS CO
  • [6] Orbital varieties of the minimal orbit[J]. Joseph, A. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 1998(01)
  • [7] The set of abelian ideals of a Borel subalgebra, cartan decompositions, and discrete series representations[J]. Kostant, B. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 1998(05)
  • [8] Spherical orbits and Abelian ideals[J]. Panyushev, D;Röhrle, G. ADVANCES IN MATHEMATICS, 2001(02)
  • [9] The poset of positive roots and its relatives[J]. Panyushev, DI. JOURNAL OF ALGEBRAIC COMBINATORICS, 2006(01)
  • [10] Short antichains in root systems, semi-Catalan arrangements, and B-stable subspaces[J]. Panyushev, DI. EUROPEAN JOURNAL OF COMBINATORICS, 2004(01)