MIT Lie Groups Seminar

Speaker:  Oron 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).