Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras

Details Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras

2011-08-18

arxiv.org/abs/1108.3659v2

Mathematics

Rings and Algebras

Scientific paper

We study certain types of ideals in the standard Borel subalgebra of an
untwisted affine Lie algebra. We classify these ideals in terms of the root
combinatorics and give an explicit formula for the number of such ideals in
type $A$. The formula involves various aspects of combinatorics of Dyck paths
and leads to a new interesting integral sequence.

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