University of Sydney Algebra Seminar

Noah White (University of Edinburgh)

Friday 31 July, 12-1pm, Place: Carslaw 375

Cactus group actions in Schubert calculus, crystals and integrable systems

The RSK correspondence assigns a pair of standard tableaux to every element of the symmetric group. This describes a partitioning of the group into Kazhdan-Lusztig 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 Kazhdan-Lusztig cells using geometry associated to the rational Cherednik algebra. I will show how this action appears using monodromy of Schubert problems or alternatively using the Bethe ansatz for certain integrable systems.