Geometric Schur Duality of two parameter quantum group of type A

2017/01/22 by Haitao Ma, Ma, Haitao, Zongzhu Lin +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1701.06114

openalex publication_date 2017/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n)

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