Research on the difference systems associated with multivariable elliptic hypergeometric functions with Weyl group symmetry

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400118
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: University of the Ryukyus (2017); Tokyo Denki University (2013-2016)
• Principal Investigator: ITO Masahiko 琉球大学, 理学部, 教授 (30348461)
• Co-Investigator(Renkei-kenkyūsha): NOUMI Masatoshi 神戸大学, 理学研究科, 教授 (80164672) ; OKADA Soichi 名古屋大学, 多元数理科学研究科, 教授 (20224016) ; KANEKO Jouichi 琉球大学, 理学部, 教授 (10194911)
• Research Collaborator: FORRESTER Peter J. メルボルン大, 理学部, 教授
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 楕円超幾何関数 / 楕円セルバーグ積分 / 楕円ガンマ関数 / 楕円補間関数 / ワイル群対称性 / 差分方程式系 / マクドナルド定数項恒等式

Outline of Final Research Achievements

The multivariable elliptic hypergeometric functions associated with root systems were studied via their systems of difference equations and Weyl group symmetry. Masahiko Ito (the leader of this research, Univ. of the Ryukyus) and Masatoshi Noumi (cooperating researcher of this research, Kobe univ.) provided a definition of the family of ``interpolation functions'' for the multivariable elliptic hypergeometric functions of type BCn. This is the main result of this research. As applications of the interpolation functions, several summation and translation formulae for the multivariable elliptic hypergeometric functions of type BCn were proved.

Free Research Field

特殊関数論