Abstract:
Using the combinatorial description of the standard Gaitsgory centralobject of the (extended, graded) affine type A Hecke category due to Elias, we
show the existence of and explicitly describe the unique endomorphism that lifts
right multiplication by the i-th fundamental weight on the i-th component of
the associated graded of its Wakimoto filtration. We give work in progress on
describing a conjectural program to categorify the Vershik-Okounkov approach
to the representation theory of the affine Hecke algebra. Here this endomorphism
will play a role. This is the affine version of the program described by Gorsky, Negut, and Rasmussen in finite type A.