Quantum twist maps and dual canonical bases
arXiv:1604.07748 · doi:10.1007/s10468-017-9729-5
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.
13 pages, minor revision, to appear in Algebras and Representation Theory