Academic Report of School of Mathematical Sciences [2026] No. 041

(Series Report for High-Level University Construction No. 1300)

Title：Diagrammatic Presentations of Affine and Cyclotomic q-Schur Algebras via Web Categories

Speaker：Linliang Song (Tongji University)

Time：14:00-16:00, May. 14, 2026

Location：Tencent Meeting 896-768-630

Abstract：In this talk, we introduce the affine q-web and Schur categories of type A, along with their cyclotomic quotients. These categories provide the first diagrammatic presentations for a broad class of algebras, including affine q-Schur algebras, higher-level affine Schur algebras, and cyclotomic q-Schur algebras. Furthermore, these categories (and their module categories) will serve as a natural framework for the categorification of the negative half of quantum affine gl_n and its integrable highest weight modules. This is joint work with Yaolong Shen and Weiqiang Wang.

Speaker Profile：Linliang Song is an associate professor in the School of Mathematical Sciences at Tongji University. His research focuses on representation theory and Lie theory, including the categorification and Schur–Weyl duality, Lie (and super) algebras, quantum groups, (affine and cyclic) Hecke algebras, and (quantum walled) Brauer algebras. He has led research projects funded by the National Natural Science Foundation of China, including General Projects and Young Scientist Projects. His research findings have been published in international journals such as Adv. Math., Math. Z., and J. Algebra.

Faculty and students are welcome to attend!

Invited by: Jinkui Wan

School of Mathematical Sciences

May 8, 2026