2008/03/15 by Hitoshi Konno · 16 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cellular algebra #Heisenberg group #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Quantum affine algebra #Quantum group #Realization (probability) #Tensor product #hep-th #math-ph #math.MP #math.QA #msc:17B37 #msc:81R10 #nlin.SI
paper · pdf · doi:10.1016/j.geomphys.2009.07.012
published in Journal of Geometry and Physics 59(11), 1485-1511 (Elsevier BV) · 42 pages
arxiv created 2008/03/15 · openalex publication_date 2009/07/31 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra Uq,p(sl2). The algebra Uq,p(sl2) has a constructive definition in terms of the Drinfeld generators of the quantum affine algebra Uq(sl2) and a Heisenberg algebra. This yields a systematic construction of both finite and infinite-dimensional dynamical representations and their parallel structures to Uq(sl2). In particular we give a classification theorem of the finite-dimensional irreducible pseudo-highest weight representations stated in terms of an elliptic analogue of the Drinfeld polynomials. We also investigate a structure of the tensor product of two evaluation representations and derive an elliptic analogue of the Clebsch-Gordan coefficients. We show that it is expressed by using the very-well-poised balanced elliptic hypergeometric series 12V11.