Two boundary Hecke algebras and combinatorics of type C

Abstract

This paper gives a Schur–Weyl duality approach to the representation theory of the affine Hecke algebras of type C with unequal parameters. The first step is to realize the affine braid group of type Ck as the group of braids on k strands with two poles. Generalizing familiar methods from the one pole (type A) case, this provides commuting actions of the quantum group Uqg and the affine braid group of type Ck on a tensor space M ⊗ N ⊗ V⊗k . Special cases provide Schur–Weyl pairings between the affine Hecke algebra of type Ck and the quantum group of type gln, resulting in natural labelings of many representations of the affine Hecke algebras of type C by partitions. Following an analysis of ..