Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type
数学专题报告
报告题目(Title)：Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type
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）16:00-17:00
邀请人(Inviter)：肖杰、覃帆、周宇
报告摘要
In this report, we discuss factorization properties of the generalized minors introduced by Fomin-Zelevinsky in the coordinate rings of Kac-Moody open Richardson varieties. By studying the simple factors of these minors in the monoidal category $\mathcal{C}_{w,v}$, we relate the cluster algebra structures on open Richardson varieties to the categorical framework developed by Kashiwara-Kim-Oh-Park. In particular, we show that cluster monomials in the coordinate ring of a Kac-Moody open Richardson variety correspond to isomorphism classes of simple modules in $\mathcal{C}_{w,v}$. As a consequence, the Grothendieck ring $K_0({\widetilde{\mathcal{C}}}_{w,v})$ contains the cluster algebra structure on the coordinate ring constructed by Bao-Ye. In finite type, we further prove that Leclerc's seeds coincide with Ménard's seeds for open Richardson varieties, and that the category ${\widetilde{\mathcal{C}}}_{w,v}$ provides a monoidal categorification of the corresponding cluster structure.
