| Résume||Berenstein, Fomin and Zelevinsky introduced biregular automorphisms, called twist automorphisms, on unipotent cells in their study of total positivity criteria. These automorphisms are essentially used for describing the inverses of specific embeddings of tori into unipotent cells, and the resulting descriptions are called the Chamber Ansatz.
In this talk, I explain a quantum analogue of their story. Namely, we construct twist automorphisms on arbitrary quantum unipotent cells and provide a quantum analogue of the Chamber Ansatz formulae. We also study our quantum analogues from the viewpoint of the quantum cluster algebra structures on quantum unipotent cells, which are deduced by Geiss- Leclerc-Schroer and Goodearl-Yakimov.
A part of this talk is based on joint work with Yoshiyuki Kimura.|