B-stable ideals in the nilradical of a Borel subalgebra

Abstract

We count the number of strictly positive $B$-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any $B$-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also compute the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.

arXiv commentWe correct the lemmas in Section 3 in the earlier version

References in corpus (1)

• Ad-nilpotent ideals of a Borel subalgebra: generators and duality

Cited by in corpus (4)

• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra
• Spherical nilpotent orbits and abelian subalgebras in isotropy representations
• Lyashko-Looijenga morphisms and primitive factorizations of the Coxeter element
• Weight posets associated with gradings of simple Lie algebras, Weyl groups, and arrangements of hyperplanes