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

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