Categorifying the integrable modules of quantum affine gl_p

Weiqiang Wang (Charlottesville, VA)

October 23, 2026

Abstract: Cyclotomic q-web categories (introduced jointly with Yaolong Shen and Linliang Song) have produced new Schur algebras sitting in between cyclotomic Hecke algebras and cyclotomic q-Schur algebras. We will explain that a module category over the path algebra of a cyclotomic q-web category 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. This generalizes the classic works of Lascoux-Leclerc-Thibon, Ariki, and Varagnolo-Vasserot. Based on joint work with Linliang Song..