The Chamber Ansatz for quantum unipotent cells

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.
Comment: v1: 17 pages, v2: 22pages. We have attached an appendix in which the explicit relation between the Feigin maps and the quantum torus embeddings given by Cauchon generators is explained. Remark 3.6 and Corollary 3.7 have been detailed. To appear in Transformation Groups