Hypergeometric functions over finite fields and representations of \(\mathrm{SL}(2,q)\)
type: Item
instance of: scholarly article
title: Hypergeometric functions over finite fields and representations of \(\mathrm{SL}(2,q)\)
zbMATH Open document ID: 0806.11062
author: V. Pereyra
published in: Rocky Mountain Journal of Mathematics
publication date: 1994-04-12T00:00:00Z
review text: From the author's abstract and introduction: ``It is well known that the matrix coefficients of the representations of the discrete series of \(\mathrm{SL}(2, \mathbb{R})\) with respect to an appropriate basis are essentially hypergeometric functions. A parallel theory is presented here for the finite group \(\mathrm{SL} (2,\mathbb{F}_q)\).'' ``The organization of the paper is as follows: A construction of the principal series is given in section 2 (after a short introduction containing some historical remarks and motivation in section 1); matrix elements of these representations are given with respect to a canonical basis in section 3; these matrix elements are described in terms of hypergeometric functions over finite fields [as defined by the author in Trans. Am. Math. Soc. 301, 77--101 (1987; Zbl 0629.12017)] in section 4; this section contains also a description of how properties of hypergeometric functions over finite fields can be derived from this framework. Finally comments, questions and related presentations are given in section 5''.
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 11T24
Mathematics Subject Classification ID: 33C60
Mathematics Subject Classification ID: 11B65
zbMATH DE Number: 515189
zbMATH Keywords: Jacobi sums
zbMATH Keywords: Gauss sums
zbMATH Keywords: representations
zbMATH Keywords: discrete series
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: finite fields
reviewed by: Anna P. Helversen-Pasotto
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072576
OpenAlex ID: W2077977302
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DOI: 10.1216/RMJM/1181072576
description: scientific article; zbMATH DE number 515189