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Cuspidal $\mathfrak{sl}_n$-modules and deformations of certain Brauer tree algebras by Mazorchuk, Volodymyr; Stroppel, Catharina is a scholarly article available to read on EtoBox.

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

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.

Author

Mazorchuk, Volodymyr; Stroppel, Catharina

Published

2010

Language

EN