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.
Original language | English |
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Pages (from-to) | 4944-4959 |
Number of pages | 16 |
Journal | Communications in Algebra |
Volume | 45 |
Issue number | 11 |
DOIs | |
Publication status | Published - Nov 2 2017 |
Externally published | Yes |
Keywords
- Double-class algebras
- Gelfand pairs and zonal spherical functions
- group algebras
- representation theory of finite groups
- structure coefficients
ASJC Scopus subject areas
- Algebra and Number Theory