Quantum twist maps and dual canonical bases
Quantum Algebra
2017-08-22 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.1604.07748,
title = {Quantum twist maps and dual canonical bases},
author = {Yoshiyuki Kimura and Hironori Oya},
journal= {arXiv preprint arXiv:1604.07748},
year = {2017}
}
Comments
13 pages, minor revision, to appear in Algebras and Representation Theory