Schur-Weyl duality for $U_{v,t}(s{l}_n)$

Abstract

In \cite{fl}, the authors get a new presentation of two-parameter quantum algebra $U_{v,t}(\mathfrak{g})$. Their presentation can cover all Kac-Moody cases. In this paper, we construct a suitable Hopf pairing such that $U_{v,t}(s{l}_n)$ can be realized as Drinfeld double of certain Hopf subalgebras with respect to the Hopf pairing. Using Hopf pairing, we construct a $R$-matrix for $U_{v,t}(s{l}_n)$ which will be used to give the Schur-Weyl dual between $U_{v,t}(s{l}_n)$ and Hecke algebra $H_k(v,t)$. Furthermore, using the Fusion procedure we construct the primitive orthogonal idempotents of $H_k(v,t)$. As a corollary, we give the explicit construction of irreducible $U_{v,t}(s{l}_n)$-representations of $V^{\otimes k}$.

13 pages

References in corpus (1)

• On the idempotents of Hecke algebras