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

Sergey Arkhipov
(MATH, AU)
Seminar
Onsdag, 22 april, 2015, at 16:15-17:15, in Aud. D3 (1531-215)
Abstrakt:
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.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen