Abelian Subalgebras in Z 2 - Graded Lie Algebras and Affine Weyl Groups
نویسندگان
چکیده
Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1.
منابع مشابه
2 3 N ov 2 00 3 ABELIAN SUBALGEBRAS IN Z 2 - GRADED LIE ALGEBRAS AND AFFINE WEYL GROUPS
Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1. §
متن کامل1 1 D ec 2 00 3 ABELIAN SUBALGEBRAS IN Z 2 - GRADED LIE ALGEBRAS AND AFFINE WEYL GROUPS
Let g = g0 ⊕ g1 be a simple Z2-graded Lie algebra and let b0 be a fixed Borel subalgebra of g0. We describe and enumerate the abelian b0-stable subalgebras of g1.
متن کاملDecomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z2-graded Lie algebras
We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of certain abelian subalgebras of simple Lie algebras.
متن کاملFiltrations in Semisimple Lie Algebras, I
In this paper, we study the maximal bounded Z-filtrations of a complex semisimple Lie algebra L. Specifically, we show that if L is simple of classical type An, Bn, Cn or Dn, then these filtrations correspond uniquely to a precise set of linear functionals on its root space. We obtain partial, but not definitive, results in this direction for the remaining exceptional algebras. Maximal bounded ...
متن کاملFeigin–Frenkel center in types B, C and D
For each simple Lie algebra g consider the corresponding affine vertex algebra Vcrit(g) at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A fo...
متن کامل