Association Schemes with at Most Two Nonlinear Irreducible Characters and Applications to Finite Groups
- 5 Downloads
An irreducible character χ of an association scheme is called nonlinear if the multiplicity of χ is greater than 1. The main result of this paper gives a characterization of commutative association schemes with at most two nonlinear irreducible characters. This yields a characterization of finite groups with at most two nonlinear irreducible characters. A class of noncommutative association schemes with at most two nonlinear irreducible character is also given.
KeywordsAssociation scheme character finite group group-like scheme multiplicity nonlinear
MR(2010) Subject Classification05E30 20C15
Unable to display preview. Download preview PDF.
- Hanaki, A., Miyamoto I.: Classification of association schemes with small number of vertices, published on web: http://math.shinshu-u.ac.jp/˜hanaki/as/Google Scholar
- Zieschang, P. H.: An Algebraic Approach to Association Schemes, Lecture Notes in Math., vol. 1628, Springer, Berlin, 1996Google Scholar