Characters of table algebras and applications to association schemes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:115

Article

Xu, Bangteng

关键词: Association schemes;    Table algebras;    Closed subsets;    Normal closed subsets;    Characters;    Kernels;   

DOI  :  10.1016/j.jcta.2008.02.005

来源: Elsevier

【 摘 要 】

Hanaki [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195-201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363-369] generalized many properties of characters of finite groups to characters of association schemes. In this paper we show that many of these properties also hold for table algebras. Our approach is not to generalize the proofs in [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195-201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363-369] to table algebras, but to prove many stronger properties, and then obtain results in [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195-201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363-369] as direct consequences. (C) 2008 Elsevier Inc. All rights reserved.

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