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Quantum Twist Maps and Dual Canonical Bases

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Abstract

In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the “reverse” lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors.

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Acknowledgements

The authors would like to express our sincere gratitude to Yoshihisa Saito, the supervisor of the second author, for his helpful comments.

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Authors and Affiliations

  1. Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka, 599-8531, Japan

    Yoshiyuki Kimura

  2. Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo, 153-8914, Japan

    Hironori Oya

Authors
  1. Yoshiyuki Kimura
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  2. Hironori Oya
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Corresponding author

Correspondence to Hironori Oya.

Additional information

Presented by Kenneth Goodearl.

The work of the first author was supported by JSPS Grant-in-Aid for Scientific Research (S) 24224001. The work of the second author was supported by Grant-in-Aid for JSPS Fellows (No. 15J09231) and the Program for Leading Graduate Schools, MEXT, Japan.

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Kimura, Y., Oya, H. Quantum Twist Maps and Dual Canonical Bases. Algebr Represent Theor 21, 589–604 (2018). https://doi.org/10.1007/s10468-017-9729-5

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  • DOI: https://doi.org/10.1007/s10468-017-9729-5

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