Capelli elements of the group algebra
Naoya Yamaguchi

TL;DR
This paper introduces Capelli elements derived from modified Capelli identities for irreducible representations, providing a basis for the center of the group algebra of finite groups.
Contribution
It develops a new approach to constructing a basis of the center of the group algebra using Capelli identities for irreducible representations.
Findings
Capelli elements form a basis of the center of the group algebra
Capelli identities are adapted for irreducible representations
Provides a new algebraic framework for understanding group algebra centers
Abstract
Inspired by the Capelli identities for group determinants obtained by T\^oru Umeda, we give a basis of the center of the group algebra of any finite group by using Capelli identities for irreducible representations. The Capelli identities for irreducible representations are modifications of the Capelli identity. These identities lead to Capelli elements of the group algebra. These elements construct a basis of the center of the group algebra.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Mathematics and Applications
