A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs. Issue 11 (2nd November 2017)

• Record Type: Journal Article
• Authors: Tout, Omar
• Is Part Of: Communications in algebra. Volume 45:Issue 11(2017)
• Page Start: 4944
• Page End: 4959
• Publication Date: 2017-11-02
• Subjects: Double-class algebras -- Gelfand pairs and zonal spherical functions -- group algebras -- representation theory of finite groups -- structure coefficients; 05E15 -- 20C08; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1287273
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: After a careful consideration of some of the well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs, we were able to deduce a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coefficients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalization of the Frobenius formula which expresses the structure coefficients of the center of a finite group algebra in terms of irreducible characters.