2017/01/23 by Yanmin Yang, Yang, Yanmin, Haitao Ma +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1701.06262
openalex publication_date 2017/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In \citefl, the authors get a new presentation of two-parameter quantum algebra Uv,t(\mathfrakg). Their presentation can cover all Kac-Moody cases. In this paper, we construct a suitable Hopf pairing such that Uv,t(sln) 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 Uv,t(sln) which will be used to give the Schur-Weyl dual between Uv,t(sln) and Hecke algebra Hk(v,t). Furthermore, using the Fusion procedure we construct the primitive orthogonal idempotents of Hk(v,t). As a corollary, we give the explicit construction of irreducible Uv,t(sln)-representations of V⊗ k.