Schur-Weyl duality patterns in modern representation theory
Friday 25th November, 2016 16:00-17:00 Maths 204
I will start by recalling the classical Schur-Weyl duality between modules over the general linear group and the symmetric group. This duality has been a major theme in representation theory and has been generalized to many settings including Hecke algebras and quantum groups or Brauer algebras and orthogonal groups. A similar pattern can be discerned in the representation theory of affine Lie algebras and rational Cherednik algebras. I will explain the construction of the Suzuki functor between certain categories of modules over these algebras and relate it to Schur-Weyl duality. I will then discuss some implications focusing on highest weight structures and the geometry of Calogero-Moser spaces and opers.