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From RSK to cactus group actions on Coxeter groups

Algebra & Discrete Mathematics

Speaker: Noah White, UCLA
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Location: 1147 MSB
Start time: Mon, Oct 22 2018, 11:00AM

The cactus group is a combinatorially defined group one can attach to a Coxeter group - an asymptotic version of the braid group. Losev and Bonnafe have described an action of the cactus group on the Coxeter group which is compatible with the Kazhdan-Lusztig cells. In type A this action can be described using the RSK correspondence and Schützenberger involutions. I will describe how this can be realised geometrically and its relation to crystals for the general linear Lie algebra. I will also give an alternative description of the action on a general Coxeter group.