表示论研讨班：Weyl group symmetries of the toric variety associated with Weyl chambers

中科院数学与系统科学研究院

数学研究所

学术报告

表示论研讨班

报告人: 桂弢博士（北京国际数学中心）

题  目：Weyl group symmetries of the toric variety associated with Weyl chambers    

时  间：2024.10.17（周四）下午14:30--15:30

地  点：N818

摘  要：For any crystallographic root system, let W be the associated Weyl group, and let WP be the weight polytope (also known as the W-permutohedron) associated with an arbitrary strongly dominant weight. The action of W on WP induces an action on the toric variety X(WP) associated with the normal fan of WP, and hence an action on the rational cohomology ring H^*(X(WP). Let P be the corresponding dominant weight polytope, which is a fundamental region of the W-action on WP. We give a type uniform algebraic proof that the fixed subring H^*(X(WP))^W is isomorphic to the cohomology ring H^*(X(P)) of the toric variety X(P) associated with the normal fan of P. Notably, our proof applies to all finite (not necessarily crystallographic) Coxeter groups, answering a question of Horiguchi--Masuda--Shareshian--Song about non-crystallographic root systems. Joint with Hongsheng Hu and Minhua Liu.