Support varieties for modules over symmetric groups

On Support Varieties for Modules over Complete Intersections

Let (A, m, k) be a complete intersection of codimension c, and k̃ the algebraic closure of k. We show that every homogeneous algebraic subset of k̃c is the cohomological support variety of an A-module, and that the projective variety of a complete indecomposable maximal Cohen-Macaulay A-module is connected.

Support Varieties for Modules over Stacked Monomial Algebras

Let Λ be a finite-dimensional (D, A)-stacked monomial algebra. In this paper, we give necessary and sufficient conditions for the variety of a simple Λ-module to be nontrivial. This is then used to give structural information on the algebra Λ, as it is shown that if the variety of every simple module is nontrivial, then Λ is a D-Koszul monomial algebra. We also provide examples of (D, A)-stacke...

Spin modules for symmetric groups

On Extensions of Simple Modules over Symmetric and Algebraic Groups

Support Varieties for Quantum Groups

Given a root datum (Y,X, . . . ) and an odd integer l G.Lusztig defined a finite-dimensional Hopf algebra u over the cyclotomic field k := Q(ξ) where ξ is a primitive l−th root of unity, see [Lu1]. Suppose that l > h where h is the Coxeter number of the split reductive Lie algebra g over k associated to the root datum (Y,X, . . . ). In this case the cohomology H(u, k) of algebra u with trivial ...