Duplex Hecke Algebras of type B
Abstract
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 S_l 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 {\i}quantum groups studied by Bao-Wang in [1].
Keywords
Cite
@article{arxiv.2312.06214,
title = {Duplex Hecke Algebras of type B},
author = {Yu Xie and An Zhang and Bin Shu},
journal= {arXiv preprint arXiv:2312.06214},
year = {2023}
}
Comments
17 pages. To appear in Journal of Algebra and its Applications