Alternating group and multivariate exponential functions

2009/07/03 by Anatoly Klimyk, Klimyk, Anatoly, Jiri Patera +2
Mathematics · Physics and Astronomy · #20B30 #33E99 #42B05 #42B10 #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #math-ph #math.MP #msc:20B30 #msc:33E99 #msc:42B05 #msc:42B10

paper · pdf · doi:10.48550/arxiv.0907.0601

This paper is to appear in Groups and Symmetries: from the Neolithic Scots to John McKay, AMS-CRM Proceedings and Lectures Notes Series, eds. J. Harnad and P. Winternitz (2008)

arxiv created 2009/07/03 · openalex publication_date 2009/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and study multivariate exponential functions, symmetric with respect to the alternating group A_n, which is a subgroup of the permutation (symmetric) group S_n. These functions are connected with multivariate exponential functions, determined as the determinants of matrices whose entries are exponential functions of one variable. Our functions are eigenfunctions of the Laplace operator. By means of alternating multivariate exponential functions three types of Fourier transforms are constructed: expansions into corresponding Fourier series, integral Fourier transforms, and multivariate finite Fourier transforms. Alternating multivariate exponential functions are used as a kernel in all these Fourier transforms. Eigenfunctions of the integral Fourier transforms are obtained.

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