Quantized coordinate rings, PBW-type bases and q-boson algebras

2014/11/28 by Yoshihisa Saito, Saito, Yoshihisa
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #math.RT #msc:17B37 #msc:17B67 #msc:81R10 #msc:81R50

paper · pdf · doi:10.48550/arxiv.1411.7824

25 pages

arxiv created 2014/11/28 · arxiv updated 2014/12/01

Abstract

Recently, Kuniba, Okado and Yamada proved that the transition matrix of PBW-type bases of the positive-half of a quantized universal enveloping algebra U_q(\mathfrakg) coincides with a matrix coefficients of the intertwiner between certain irreducible modules over the corresponding quantized coordinate ring A_q(\mathfrakg), introduced by Soibelman. In the present article, we give a new proof of their result, by using representation theory of the q-boson algebra, and the Drinfeld paring of U_q(\mathfrakg).

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• Modules over quantized coordinate algebras and PBW-bases

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