A SPECIAL ENDOMORPHISM OF THE STANDARD GAITSGORY CENTRAL OBJECT OF THE AFFINE HECKE CATEGORY
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Date
2024-03-25
Authors
Hathaway, Jay
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
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.
Description
Keywords
Algebra, Algebraic Geometry, Categorification, Representation Theory