Singularities of R-matrices and E-invariants for Dynkin quivers
数学专题报告
报告题目(Title)：Singularities of R-matrices and E-invariants for Dynkin quivers
报告人(Speaker)：Ryo Fujuta （RIMS Kyoto）
地点(Place)：后主楼1124
时间(Time)：2025年5月28日 周三下午 16:00
邀请人(Inviter)：肖杰、覃帆、周宇、兰亦心
报告摘要
In the theory of finite-dimensional representations of affine quantum groups, the singularities of (normalized) R-matrices play an important role as they encode the non-commutativity of tensor product representations. However, computing the pole order of R-matrices is a difficult problem in general, and so far explicitly known only for fundamental and Kirillov-Reshetikhin modules. In this presentation, we restrict our attention to a certain subcategory of representations which monoidally categorifies a cluster algebra of finite type (known as Hernandez-Leclerc’s level-one subcategory), and explain that the pole order of R-matrices is computable for any irreducible representations as the dimension of E-invariants (analog of extension groups) of decorated representations of Dynkin quivers. This manifests a correspondence of numerical characteristics between monoidal and additive categorifications of cluster algebras of finite type.
