Table Algebras with Exactly One Irreducible Character whose Degree and Multiplicity are Not Equal

Department

Mathematics and Statistics

Document Type

Article

Publication Date

12-2017

Abstract

Commutative standard table algebras with exactly one multiplicity not equal to 1 are characterized by the wreath product of some special table algebras in [1]. A natural and much more general question is the characterization of standard table algebras (not necessarily commutative) with exactly one irreducible character whose degree and multiplicity are not equal and the degree is 1. We will give a characterization of such table algebras, including the main result of [1] as a special case. Applications to association schemes are also discussed.

Journal Title

Communications in Algebra

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