Remarks on quantum unipotent subgroup and dual canonical basis

TL;DR

This paper proves a conjecture about the tensor product decomposition of a quantum algebra related to Weyl groups, advancing understanding of dual canonical bases in quantum groups.

Contribution

It establishes the tensor product decomposition of a quantum unipotent subgroup, confirming a conjecture by Berenstein and Greenstein.

Findings

Proved the tensor product decomposition conjecture.

Enhanced understanding of dual canonical bases.

Connected quantum group structures with Weyl group elements.

Abstract

We prove the tensor product decomposition of the half of quantized universal enveloping algebra associated with a Weyl group element which was conjectured by Berenstein and Greenstein.