2023/12/11 by Yu Xie, An Zhang, Xie, Yu +3
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2312.06214
As a sequel to [14], in this article we first introduce a so-called duplex Hecke algebras of type B which is a Q(q)-algebra associated with the Weyl group W (B) of type B, and symmetric groups Sl for l = 0, 1, . . . ,m, satisfying some Hecke relations. This notion originates from the degenerate duplex Hecke algebra arising from the course of study of a kind of Schur-Weyl duality of Levi-type, extending the duplex Hecke algebra of type A arising from the related q-Schur-Weyl duality of Levi-type. A duplex Hecke algebra of type B admits natural representations on certain tensor spaces. We then establish a Levi-type q-Schur-Weyl duality of type B, which reveals the double centralizer property between such duplex Hecke algebras and ıquantum groups studied by Bao-Wang in [1].