On the Index of the Quotient of a Borel Subalgebra by an ad-Nilpotent Ideal
Copyright policy )On the Index of the Quotient of a Borel Subalgebra by an ad-Nilpotent Ideal
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.
15 pages
index, 17B05, 17B20, Borel subalgebras, Coadjoint orbits; nilpotent varieties, 17B05; 17B20, ad-nilpotent ideals, FOS: Mathematics, Root systems, Representation Theory (math.RT), Simple, semisimple, reductive (super)algebras, Mathematics - Representation Theory
index, 17B05, 17B20, Borel subalgebras, Coadjoint orbits; nilpotent varieties, 17B05; 17B20, ad-nilpotent ideals, FOS: Mathematics, Root systems, Representation Theory (math.RT), Simple, semisimple, reductive (super)algebras, Mathematics - Representation Theory
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