Geometric Schur Duality of two parameter quantum group of type A

Abstract

In this paper, we give an geometric description of the Schur-Weyl duality for two-parameter quantum algebras $U_{v,t}(g{l}_n)$, where $U_{v,t}(g{l}_n)$ is the deformation of $U_v(I,\cdot )$, the classic Shur-Weyl duality $(U_{r,s}(g{l}_n),V^{\otimes d},H_d(r,s))$ can be seen as a corollary of the Shur-Weyl duality $(U_{v,t}(g{l}_n),V^{\otimes d},H_d(v,t))$ by using the galois descend approach. we also establish the Shur-Weyl duality between the algebras $\widetilde{U_{v,t}(g{l}_N{)}^m}$, $\widehat{U_{v,t}(g{l}_N{)}^m}$ and Heck algebra $H_k(v,t)$.

26 papes, No figures. This is a draft of the first paper of our series papers on geometric Schur Duality of two parameter quantum groups. arXiv admin note: substantial text overlap with arXiv:1408.6740 by other authors

Cited by in corpus (1)

• Geometric RTT realization of $U_v(g{l}_n{)}^{+}$