ad-Nilpotent ideals of a Borel subalgebra II

Details ad-Nilpotent ideals of a Borel subalgebra II ad-Nilpotent ideals of a Borel subalgebra II

2001-06-08

arxiv.org/abs/math/0106057v2

J. Algebra 258 (2002), no. 1, 112--121.

Mathematics

Representation Theory

AMS-TeX file, 9 pages; revised version. To appear in Journal of Algebra

Scientific paper

We provide an explicit bijection between the ad-nilpotent ideals of a Borel
subalgebra of a simple Lie algebra g and the orbits of \check{Q}/(h+1)\check{Q}
under the Weyl group (\check{Q} being the coroot lattice and h the Coxeter
number of g). From this result we deduce in a uniform way a counting formula
for the ad-nilpotent ideals.

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