- 可积系统黑板讨论班

Bounds on dimensions of spaces of homomorphisms for products of affine $\mathfrak{sl}_2$-evaluation modules

组织者

安德烈·利亚希克 , 尼古拉·莱舍提金 , 许睿捷

演讲者

Andrei Grigorev

时间

2026年05月25日 15:30 至 16:30

地点

A7-201

摘要

Affine quantum groups are certain $q$-deformations of the corresponding universal enveloping algebras. Irreducible finite-dimensional representations of affine quantum groups corresponding to affinizations of algebras of classical types were classified in 90's. However, many questions about finite-dimensional representations remain unanswered. In our work we are interested in dimensions of the spaces of homomorphisms between tensor products of certain modules over affine quantum $\mathfrak{sl}_2$ depending on parameters. We obtain bounds for these dimensions in terms of combinatorial objects related to the sequences of the parameters of modules in the tensor products. The talk is based on work joint with E. Mukhin.