Speaker: 桂弢博，北京国际数学中心

Inviter: 聂思安研究员

Title: Weyl group symmetries of the toric variety associated with Weyl chambers

Language: English

Time & Venue: 2024.10.17 14:30-15:30 N818

Abstract: 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.