Seminar:
Geometry, Symmetry and Physics
Event time:
Friday, April 4, 2025 - 4:00pm to 6:00pm
Speaker:
Quan Situ
Speaker affiliation:
Université Clermont Auvergne
Event description:
The BGG category O plays an important role in the study of representations of semisimple Lie algebras. Its connection to the Hecke category is a starting point of Geometric Representation Theory. In this lecture, I will introduce a version of category O for quantum groups at roots of unity. I will explain a derived equivalence from (the principal block of) quantum category O to the affine Hecke category. Under the equivalence, the highest weight structure of quantum category O provides a categorification of the “periodic Hecke module”.
In the third lecture, I will introduce the main result on an equivalence between quantum category O and affine Hecke category. Then I will explain the corresponding t-structure on the affine Hecke category, and its relation to the periodic Hecke module.
Research Area(s):
Representation Theory
Special note:
Seminar talk is supported in part by the Mrs. Hepsa Ely Silliman Memorial Fund.