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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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
Keywords
- Quantized universal enveloping algebras
- Quantum twist maps
- Dual canonical bases
- Poincaré-Birkhoff-Witt type bases
- Unipotent quantum minors
- Quantum T-systems