Seminar: Sergey Arkhipov (AU)

Title: Quantum Schur-Weyl correspondence, quantum groups at q=0, and categorification of 0-Schur algebras

2015.04.14 | Jane Jamshidi

Date Wed 22 Apr
Time 16:15 17:15
Location 1531-215 (Aud. D3)


We recall the classical Schur-Weyl duality and interpret it in terms of cohomology of partial Flag varieties. Next we recall Springer correspondence for GL(n) following Ginzburg and Vasserot: we realize quantum affine Schur algebras as equivariant K-groups of the corresponding Steinberg type variety. 

We consider Gl(n)-orbits in the variety of pairs of d-step flags in the standard n-dimensional vector space. Following Jensen and Su we introduce the generic convolution algebra and compare it to a quotient algebra of the q=0 version of the quantum group for gl(n) due to Thibon at all.

We replace combinatorics by geometry and define the affine 0-Schur algebra as the corresponding equivariant K-group with convolution product. We prove a version of Schur-Weyl duality in this setting. 

Finally we define quasi-coherent Schur category with the monoidal structure given by convolution and prove that q=0 Serre relations hold in it without passing to the level of Grothendieck groups.