OIST Representation Theory Seminar

Speaker: Stephen Doty, Loyola University Chicago

Title: Schur-Weyl duality for braid and twin groups via the Burau representation

Abstract: The natural permutation representation of the symmetric group admits a q-analogue known as the Burau representation. The symmetric group admits two natural covering groups: the braid group of Artin and the twin group of Khovanov, obtained respectively by forgetting the cubic and quadratic relations in the Coxeter presentation of the symmetric group. By computing centralizers of tensor powers of the Burau representation, we obtain new instances of Schur-Weyl duality for braid groups and twin groups, in terms of the partial permutation and partial Brauer algebras. The method produces many representations of each group that can be understood combinatorially. (This is joint work with Tony Giaquinto.)