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arXiv · 1604.07748

Quantum twist maps and dual canonical bases

Yoshiyuki Kimura·Hironori Oya
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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 Poincar\'e-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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BibTeXRIS

Yoshiyuki Kimura, Hironori Oya. 2016-04-26. Quantum twist maps and dual canonical bases. https://doi.org/10.1007/s10468-017-9729-5

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