Cuspidal $\mathfrak{sl}_n$-modules and deformations of certain Brauer tree algebras

Details Cuspidal $\mathfrak{sl}_n$-modules and deformations of certain Brauer tree algebras Cuspidal $\mathfrak{sl}_n$-modules and deformations of certain Brauer tree algebras

2010-01-15

arxiv.org/abs/1001.2633v1

Advances in Mathematics, Volume 228, Issue 2, 2011, Pages 1008-1042

Mathematics

Representation Theory

36 pages

Scientific paper

We show that the algebras describing blocks of the category of cuspidal weight (respectively generalized weight) $\mathfrak{sl}_n$-modules are one-parameter (respectively multi-parameter) deformations of certain Brauer tree algebras. We explicitly determine these deformations both graded and ungraded. The algebras we deform also appear as special centralizer subalgebras of Temperley-Lieb algebras or as generalized Khovanov algebras. They show up in the context of highest weight representations of the Virasoro algebra, in the context of rational representations of the general linear group and Schur algebras and in the study of the Milnor fiber of Kleinian singularities.

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