The RSK correspondence assigns a pair of standard tableaux to every element of the symmetric group. This describes a partitioning of the group into “cells”. More generally these cells can be defined for any Coxeter group. Recently Henriques and Kamnitzer defined an action of the “cactus group” on crystals for semisimple Lie algebras. I will explain, in type A, the connection between this action and a conjectural method of Bonnafe and Rouquier of defining cells for the symmetric group. I will show how this action appears using Schubert calculus or alternatively using the representation theory of the symmetric group and certain generalisations of the Jucys-Murphy elements called the Gaudin Hamiltonians.
Schubert calculus and the cactus group
Noah White (Edinburgh)
Mon, 16/02/2015 - 16:30