Categorifying quantum affine gl_p and its integrable modules

Abstract: Cyclotomic q-webs (introduced recently joint with Linliang Song and Yaolong Shen) have produced new algebras sitting in between cyclotomic Hecke algebras and cyclotomic q-Schur algebras. We will explain that a module category over the cyclotomic q-web for q a root of unity categorifies an integrable highest weight module over quantum affine gl_p, and the projective indecomposable modules categorify the canonical basis. To that end, we connect the affine q-webs to Hall algebra of the cyclic quiver and to geometric representation theory. This generalizes the classic works of Lascoux-Leclerc-Thibon, Ariki, and Varagnolo-Vasserot. Based on joint work with Linliang Song.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.