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Weyl group symmetries of the toric variety associated with Weyl chambers

组织者

沈大立

演讲者

Tao Gui

时间

2024年11月19日 15:00 至 16:00

地点

A3-3-301

线上

Zoom 230 432 7880 (BIMSA)

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. I will also explain why our proof applies to non-crystallographic Coxeter groups, in which case there is no toric variety but the “virtual cohomology rings” exist. Joint with Hongsheng Hu and Minhua Liu.

演讲者介绍

I got my Ph. D. in 2023 from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Currently I am a postdoc of the Beijing International Center for Mathematical Research, Peking University. My research interests are Lie theory, geometric/combinatorial representation theory, and combinatorial Hodge theory. And I have broad interests in topological, geometric, and combinatorial problems related to representation theory.