Japanese Journal of Mathematics

, Volume 10, Issue 1, pp 97–104

Appendix: On some Gelfand pairs and commutative association schemes

Original Article

DOI: 10.1007/s11537-014-1391-7

Cite this article as:
Bannai, E. & Tanaka, H. Jpn. J. Math. (2015) 10: 97. doi:10.1007/s11537-014-1391-7


This paper is Appendix of the paper of T. Ceccherini-Silberstein, F. Scarabotti and F. Tolli [8].

We pay close attention on a special condition related to Gelfand pairs. Namely, we call a finite group G and its automorphism \({\sigma}\) satisfy Condition (\({\bigstar}\)) if the following condition is satisfied: if for \({x,\,y\,\in G}\), \({x\,\cdot\, x^{-\sigma}}\) and \({y\,\cdot\, y^{-\sigma}}\) are conjugate in G, then they are conjugate in \({K=C_G(\sigma)}\). The main purpose of the note was to study the meanings of this condition, as well as showing many examples of G and \({\sigma}\) which do (or do not) satisfy Condition (\({\bigstar}\)).

Keywords and phrases

Gelfand pair commutative association scheme 

Mathematis Subject Classification (2010)

20B05 20G40 05E30 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2014

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Research Center for Pure and Applied Mathematics, Graduate School of Information SciencesTohoku UniversitySendaiJapan