Quantum Twist Maps and Dual Canonical Bases
Quantum Twist Maps and Dual Canonical Bases
复制标题
量子扭曲图和双规范基
DOI：
10.1007/s10468-017-9729-5
复制
发表时间：
2017
影响因子：
0.6
通讯作者：
Oya Hironori
中科院分区：
文献类型：
--
作者：
Kimura Yoshiyuki;Oya Hironori
本文证明了由Lenagan-Yakimov引入的量子扭曲映射诱导量子幂零子代数的对偶标准基之间的双射。作为推论，我们证明了在“逆”字典序下对偶标准基与Poincaré-Birkhoff-Witt型基之间的单三角性.我们还表明，量子扭曲映射诱导某些幂幺量子子之间的双射。
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.