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Spherical Functions on Projective Class Algebras

최은미
대한수학회 (The Korean Mathematical Society)|2006.02|대한수학회보 (Bulletin of the KMS)|제43권 제1호|pp. 189-212

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Abstract

Let $F^\alpha G$ be a twisted group algebra with basis $\{u_g |g \in G\}$ and ${\mathcal P}= \{ {\mathcal C}_g | g \in G \}$ be a partition of $G$. A projective class algebra associated with ${\mathcal P}$ is a subalgebra of $F^\alpha G$ generated by all class sums $\sum_{x \in {\mathcal C}_g} u_x$. A main object of the paper is to find interrelationships of projective class algebras in $F^\alpha G$ and in $F^\alpha H$ for $H<G$. And the $\alpha$-spherical function will play an important role for the purpose. We find functional properties of $\alpha$-spherical functions and investigate roles of $\alpha$-spherical functions as characters of projective class algebras.

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관련 논문AI추천

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