1996/10/24 by P. Stovicek, Pavel 艩钮ov谋虂膷ek, Reidun Twarock +1
Mathematics 路 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.QA #q-alg
paper 路 pdf 路 doi:10.1063/1.531808
LaTeX file, JMP (to appear)
arxiv created 1996/10/24 路 openalex publication_date 1997/02/01 路 arxiv updated 2009/11/30 路 openalex created_date 2019/06/27 路 openalex updated_date 2026/07/28
A relationship between quantum flag and Grassmann manifolds is revealed. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a homomorphism leads to a left 饾挵h(饾敯饾敳(N))-module structure on the algebra generated by quantum antiholomorphic coordinate functions living on the flag manifold. The module is defined by prescribing the action on the unit and then extending it to all polynomials using a quantum version of the Leibniz rule. The Leibniz rule is shown to be induced by the dressing transformation. For discrete values of parameters occurring in the diagonalization one can extract finite-dimensional irreducible representations of 饾挵h(饾敯饾敳(N)) as cyclic submodules.