# The Chamber Ansatz for quantum unipotent cells

## TL;DR

This paper establishes quantum analogues of the Chamber Ansatz for unipotent cells, linking quantum twist automorphisms with dual canonical bases and generalizing previous automorphisms in quantum algebra.

## Contribution

It introduces quantum versions of the Chamber Ansatz formulae and connects quantum twist automorphisms to dual canonical bases, extending prior automorphism constructions.

## Key findings

- Quantum analogues of Chamber Ansatz formulae are proven.
- Quantum twist automorphisms are shown to generalize Berenstein-Rupel's automorphisms.
- Compatibility with dual canonical bases is confirmed.

## Abstract

In this paper, we prove quantum analogues of the Chamber Ansatz formulae for unipotent cells. These formulae imply that the quantum twist automorphisms, constructed by Kimura and the author, are generalizations of Berenstein-Rupel's quantum twist automorphisms for unipotent cells associated with the squares of acyclic Coxeter elements. This conclusion implies that the known compatibility between quantum twist automorphisms and dual canonical bases corresponds to the property conjectured by Berenstein and Rupel.