ON SCHUR-WEYL DUALITY, A_n HECKE ALGEBRAS AND QUANTUM sl(N) ON $\otimes^{n+1}{\mathbb C}^N$

Abstract

We prove that an N-state vertex model representation of the A n Hecke algebra quotient NH n (q) is faithful for all q. We use the result to examine the indecomposable content of these representations, and hence the structure of the centraliser algebra, which is generically a quotient of U q sl(N), at q a root of unity. We achieve a complete analysis in the case N=2, finding a number of Morita self-dual algebraic structures.