Representation of elliptic quantum groups and elliptic Ruijsenaars model

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400046
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tokyo University of Marine Science and Technology
• Principal Investigator: Konno Hitoshi 東京海洋大学, 学術研究院, 教授 (00291477)
• Co-Investigator(Renkei-kenkyūsha): JIMBO MICHIO 立教大学, 理学部, 教授 (80109082) ; NOUMI MASATOSHI 神戸大学, 大学院理学研究科, 教授 (80164672) ; MIMACHI KATSUHISA 大阪大学, 大学院情報科学研究科, 教授 (40211594) ; OSHIMA KAZUYUKI 愛知工業大学, 基礎教育センター, 准教授 (30547980)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 楕円量子群 / 楕円Ruijsenaars模型 / 楕円q-KZ方程式 / 量子行列式 / 変形W代数 / Macdonald対称関数 / 楕円超幾何関数

Outline of Final Research Achievements

We have formulated the quantum determinant as well as the quantum minor determinants of the L-operators for the face type elliptic quantum group U_q,p(gl_N). We have also obtained a formula for the elliptic half currents in terms of the quantum minor determinants. We then have completed a proof of the isomorphism between U_q,p(gl_N) and the central extension E_q,p(gl_N) of Felder’s elliptic quantum group. In addition, we have obtained formal elliptic hypergeometric integral solutions to the face type elliptic q-KZ equation and associated elliptic weight functions by considering the traces of the product of the intertwining operators of the level-1 U_q,p(sl_N)-modules.

Free Research Field

数理物理学、表現論