2025/02/20 by Masaki Kashiwara, Toshiki Nakashima, Kashiwara, Masaki +1
Mathematics · Physics and Astronomy · #05E10 #16D90 #16T20 #17B37 #18M05 #18M15 #81R10 #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2502.14319
openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A localized quantum unipotent coordinate category \widetilde\mathscrCw associated with a Weyl group element w is a rigid monoidal category which is obtained by applying the localization process to a subcategory of the category of finite-dimensional graded modules of a quiver Hecke algebra. We shall show that the family of the isomorphism classes (up to grading shifts) of simple objects in \widetilde\mathscrCw possesses a crystal structure and it is isomorphic to the cellular crystal associated with w. As an application of this result, we shall show the connectedness of the crystal graph of an arbitrary cellular crystal.