Title：Hall polynomials of affine type

Abstract：Classical Hall polynomials introduced independently by Steinitz and Hall have a close relation with Hall-Littlewood functions and play important roles in the study of representations of symmetric groups and general linear groups. In the 1990s, Ringel defined Hall numbers for representations of quivers over finite fields and proved that in the Dynkin quiver case, Hall numbers are indeed integer polynomials of the cardinalities of ground fields. We prove that Hall polynomial exists for each triple of decomposition sequences associated with affine quivers with automorphism (or, equivalently, all tame hereditary algebras over finite fields). This talk is based on joint work with Shiquan Ruan and Lina Han

Speaker：Bangming Deng，Tsinghua University

Date：9:30am-10:30am  2024-6-1

Venue: Room 208，School of Mathematical Science

Organizer：School of Mathematical Science

Students and teachers are welcome.