Quantum twist maps and dual canonical bases

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.