SPHERICAL FUNCTIONS ON PROJECTIVE CLASS ALGEBRAS

Title & Authors
SPHERICAL FUNCTIONS ON PROJECTIVE CLASS ALGEBRAS
Choi, Eun-Mi;

Abstract
Let $\small{F^{\alpha}G}$ be a twisted group algebra with basis $\small{{{\mu}g|g\;{\in}\;G}}$ and $\small{P\;=\;{C_g|g\;{\in}\;G}}$ be a partition of G. A projective class algebra associated with P is a subalgebra of $\small{F^{\alpha}G}$ generated by all class sums $\small{\sum\limits{_{x{\in}C_g}}\;{\mu}_x}$. A main object of the paper is to find interrelationships of projective class algebras in $\small{F^{\alpha}G}$ and in $\small{F^{\alpha}H}$ for H < G. And the a-spherical function will play an important role for the purpose. We find functional properties of a-spherical functions and investigate roles of $\small{\alpha-spherical}$ functions as characters of projective class algebras.
Keywords
spherical functions;group characters;
Language
English
Cited by
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