Remarks on quantum unipotent subgroups and the dual canonical basis

Yoshiyuki Kimura

Vol. 286 (2017), No. 1, 125–151

DOI: 10.2140/pjm.2017.286.125

Abstract

We prove the tensor product decomposition of the half of the quantized universal enveloping algebra associated with a Weyl group element which was conjectured by Berenstein and Greenstein (preprint, 2014, arXiv 1411.1391; see Conjecture 5.5)

using the theory of the dual canonical basis. In fact, based on the compatibility between the decomposition and the dual canonical basis, a weak multiplicity-free property between the factors is established.

Keywords

quantum groups, dual canonical basis

Mathematical Subject Classification 2010

Primary: 17B37, 13F60

Milestones

Received: 7 July 2015

Revised: 28 May 2016

Accepted: 29 May 2016

Published: 9 December 2016