Ad-nilpotent ideals of a Borel subalgebra II

[摘要] We provide an explicit bijection between the ad-nilpotent ideals of a Borel subalgebra. of a simple Lie algebra g and the orbits of Q/(h + 1) 6 under the Weyl group (Q being the coroot lattice and It the Coxeter number of g). From this result we deduce in a uniform way a counting formula for the ad-nilpotent ideals. (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-12-01

[关键词] ad-nilpotent ideal;Lie algebra;order ideal;hyperplane arrangement;Weyl group;affine Weyl group