TY - JOUR
T1 - THE CHAMBER ANSATZ FOR QUANTUM UNIPOTENT CELLS
AU - Oya, Hironori
N1 - Funding Information:
∗The work of the author was supported by Grant-in-Aid for JSPS Fellows (No. 15J09231) and the Program for Leading Graduate Schools, MEXT, Japan. It was also supported by the European Research Council under the European Union’s Framework Programme H2020 with ERC Grant Agreement number 647353 Qaffine, during the revision of this paper. Received February 2, 2017. Accepted August 16, 2018. Published online October 25, 2018. Corresponding Author: Hironori Oya, e-mail: oya@ms.u-tokyo.ac.jp
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/3/15
Y1 - 2019/3/15
N2 - 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.
AB - 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.
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U2 - 10.1007/s00031-018-9500-y
DO - 10.1007/s00031-018-9500-y
M3 - Article
AN - SCOPUS:85055747245
SN - 1083-4362
VL - 24
SP - 193
EP - 217
JO - Transformation Groups
JF - Transformation Groups
IS - 1
ER -