On the index of the quotient of a Borel subalgebra by an ad-nilpotent ideal

Abstract

In this paper, we give upper bounds for the index of the quotient of the Borel subalgebra of a simple Lie algebra or its nilpotent radical by an ad-nilpotent ideal. For the nilpotent radical quotient, our bound is a generalization of the formula for the index given by Panov in the type A case. In general, this bound is not exact. Using results from Panov, we show that the upper bound for the Borel quotient is exact in the type $A$ case, and we conjecture that it is exact in general.

arXiv comment15 pages

References in corpus (1)

• On index of certain nilpotent Lie algebras

Cited by in corpus (1)

• Affine slice for the coadjoint action of a class of biparabolic subalgebras of a semisimple Lie algebra