Understanding of the relation between degenerate hypergeometric functions and the matrix coefficients of the discrete series representations of semi simple Lie groups

Research Project

Project/Area Number	23540005
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Algebra
Research Institution	Yamagata University
Principal Investigator	HAYATA Takahiro 山形大学, 理工学研究科, 准教授 (50312757)
Project Period (FY)	2011-04-28 – 2015-03-31
Project Status	Completed (Fiscal Year 2014)
Budget Amount *help	¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000) Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords	半単純リー群 / 超幾何関数 / 行列係数 / 離散系列 / 保型形式 / 基本領域
Outline of Final Research Achievements	The special unitary group SU(3,1) of index (3,1) which is real rank 1 has so called the large discrete series representation as well as the (anti-)holomorphic ones. The matrix coefficients of the holomorphics are well known. In this study, we obtained the radial part of the matrix coefficients of the large discrete series at the minimal K types using generalized hypergeometric functions. We also revealed that these are actually a combination of logarithm function and the rational functions with binomial coefficients by way of degeneracy of parameters.

Report

(5 results)