Quantum twist maps and dual canonical bases (Various Issues relating to Representation Theory and Non-commutative Harmonic Analysis)

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  • Oya, Hironori
    Graduate School of Mathematical Sciences, The University of Tokyo

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  • Quantum twist maps and dual canonical bases

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Abstract

In this report, we explain our results on the compatibility between quantum twist maps and dual canonical bases. The quantum twist maps that we deal with are introduced by Lenagan-Yakimov [LeY], and they are algebra anti-automorphisms on quantized enveloping algebras. We show that they induce bijections between dual canonical bases if we regard them as anti-isomorphisms between quantum nilpotent subalgebras. As a corollary, we show certain symmetries of the entries of transition matrices between dual Poincaré-Birkhoff-Witt type bases and dual canonical bases. This report is based on joint work with Yoshiyuki Kimura.

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  • RIMS Kokyuroku

    RIMS Kokyuroku 2031 94-106, 2017-05

    京都大学数理解析研究所

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