2017/04/05 by Hideya Watanabe, Watanabe, Hideya
Mathematics · #05E10 (Secondary) #17B10 (Primary) #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1704.01277
openalex publication_date 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the representation theory of a quantum symmetric pair (U,U\jmath) with two parameters p,q of type AIII, by using highest weight theory and a variant of Kashiwara's crystal basis theory. Namely, we classify the irreducible U\jmath-modules in a suitable category and associate with each of them a basis at p=q=0, the \jmath-crystal basis. The \jmath-crystal bases have nice combinatorial properties as the ordinary crystal bases do.