2019/04/10 by Yang Shi, Shi, Yang
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Computer science #FOS: Physical sciences #Geometry #Homogeneous space #Integrable system #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Order (exchange) #Pure mathematics #Reflection (computer programming) #Type (biology) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1904.04958
arxiv created 2019/04/10 · openalex publication_date 2019/04/10 · arxiv updated 2019/04/11 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28
By considering the normalizers of reflection subgroups of types A1(1) and A3(1) in \widetildeW(D5(1)), two normalizers: \widetildeW(A3× A1)(1)\ltimes W(A1(1)) and \widetildeW(A1× A1)(1)\ltimes W(A3(1)) can be constructed from a (A3× A1× A1)(1) type subroot system. These two symmetries arose in the studies of discrete \Pa equations \citeKNY:2002, Takenawa:03, OS:18, where certain non-translational elements of infinite order were shown to give rise to discrete \Pa equations. We clarify the nature of these elements in terms of Brink-Howlett theory of normalizers of Coxeter groups \citeBH. This is the first of a series of studies which investigates the properties of discrete integrable equations via the theory of normalizers.