Towards Monoidal Categorifications of Twisted Products of Flag Varieties
数学专题报告
报告题目(Title)：Towards Monoidal Categorifications of Twisted Products of Flag Varieties
报告人(Speaker)：毕映锦（哈尔滨工程大学）
地点(Place)：后主楼1220
时间(Time)：2026年6月17日（周三）15:00-16:00
邀请人(Inviter)：肖杰、覃帆、周宇
报告摘要
Let G be a simple, simply connected, simply laced algebraic group, and let $U_q(\hat{\mathfrak{g}})$ be the corresponding quantum affine algebra. In this report, we construct a monoidal category of finite-dimensional representations of $U_q (\hat{\mathfrak{g}})$ whose Grothendieck ring contains a cluster algebra with an initial seed identified with that of the coordinate ring of twisted products of flag varieties. This construction provides a categorical framework connecting monoidal categorification and cluster structures arising from algebraic geometry. The class of varieties considered here includes, as important special cases, braid varieties and reduced double Bruhat cells. Our results therefore give a unified representation-theoretic approach to the cluster structures on these varieties.
