TY - JOUR
T1 - A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs
AU - Tout, Omar
N1 - Publisher Copyright:
© 2017 Taylor & Francis.
PY - 2017/11/2
Y1 - 2017/11/2
N2 - 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.
AB - 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.
KW - Double-class algebras
KW - Gelfand pairs and zonal spherical functions
KW - group algebras
KW - representation theory of finite groups
KW - structure coefficients
UR - http://www.scopus.com/inward/record.url?scp=85018522206&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85018522206&partnerID=8YFLogxK
U2 - 10.1080/00927872.2017.1287273
DO - 10.1080/00927872.2017.1287273
M3 - Article
AN - SCOPUS:85018522206
SN - 0092-7872
VL - 45
SP - 4944
EP - 4959
JO - Communications in Algebra
JF - Communications in Algebra
IS - 11
ER -