MIT Lie Groups Seminar

Wednesday, May 10, 2023 at 4:00pm to 5:00pm

Building 2, 2-142
182 MEMORIAL DR, Cambridge, MA 02139

SpeakerOron Propp

Title:  A coherent categorification of the asymptotic affine Hecke algebra

Abstract:  We describe a new realization of Lusztig’s asymptotic affine Hecke algebra J in terms of coherent sheaves on a moduli stack of Deligne–Langlands parameters. More precisely, we show that J arises from a certain restric-tion of the ”coherent Springer sheaf,” which is associated to the (usual) affine Hecke algebra via the categorical local Langlands correspondence. We will then explain how to ”upgrade” this sheaf-theoretic realization of J to a categorification using certain coherent sheaves on Springer fibers, following a conjecture of Qiu–Xi. Finally, we will use the asymptotic pic-ture to motivate the result, independently announced by Hemo–Zhu, that the coherent Springer sheaf lies in cohomological degree 0 (i.e., is a sheaf rather than a complex).


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