Towards a functor between affine and finite Hecke categories in type A
Massachusetts Institute of Technology. Department of Mathematics.
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In this thesis we construct a functor from the perfect subcategory of the coherent version of the affine Hecke category in type A to the finite constructible Hecke category, partly categorifying a certain natural homomorphism of the corresponding Hecke algebras. This homomorphism sends generators of the Bernstein's commutative subalgebra inside the affine Hecke algebra to Jucys-Murphy elements in the finite Hecke algebra. Construction employs the general strategy devised by Bezrukavnikov to prove the equivalence of coherent and constructible variants of the affine Hecke category. Namely, we identify an action of the category Rep(GLn) on the finite Hecke category, and lift this action to a functor from the perfect derived category of the Steinberg variety, by equipping it with various additional data.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 49-51).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.; Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology