Elias, BenHathaway, Jay2024-03-252024-03-252024-03-25https://hdl.handle.net/1794/29277Using 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.en-USAll Rights Reserved.AlgebraAlgebraic GeometryCategorificationRepresentation TheoryElectronic Thesis or Dissertation