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

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

2009-08-28

arxiv.org/abs/0908.4201v1

Journal of Lie Theory 20 (2010), 49-63.

Mathematics

Representation Theory

15 pages

Scientific paper

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.

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