Cactus group actions and cell modules

Abstract: The cactus group associated to a Coxeter group can be thought of as an asymptotic version of the braid group. It has been observed by many authors that interesting cactus group actions can be constructed in many situations when one has a representation of the braid group. In this talk I will explain what the cactus group is, and what is meant by "asymptotic". I will also explain how to construct cactus group actions associated to cell modules of the Hecke algebra, a description of this action using Lusztig’s isomorphism between the Hecke algebra and group algebra and point to some interesting questions along the way. Much of this talk is work joint with Raphael Rouquier.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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