- Date : 2022-09-27 (Tue) 15:00 ~ 16:00
- Place : Zoom
- Speaker : Shun-Jen Cheng (Academia Sinica)
- Title : Categories of Whittaker Modules over Lie superalgebras and Categorification of Fock Spaces
- Abstract :
We explain certain categories of Whittaker modules over the Lie superalgebras that can be realized as properly stratified categories. These categories turn out to be equivalent to certain Serre quotients of the BGG category O. Using this realization we show that in the case of the general linear and ortho-symplectic Lie superalgebras these Whittaker categories categorify certain q-symmetric Fock spaces over the infinite-rank quantum group of type A and certain infinite-rank quantum symmetric pairs of type AIII, respectively. In this picture, the canonical and dual canonical bases in these q-symmetric Fock spaces correspond to tilting and simple objects in these Whittaker categories, respectively. This talk is based on joint works with C.-W. Chen and V. Mazorchuk.