Appendix: On some Gelfand pairs and commutative association schemes

Eiichi Bannai; Hajime Tanaka

doi:10.1007/s11537-014-1391-7

Appendix: On some Gelfand pairs and commutative association schemes

Eiichi Bannai, Hajime Tanaka

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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 σsatisfy Condition ((Formula presented.)(Formula presented.)) if the following condition is satisfied: if for (Formula presented.)(Formula presented.), (Formula presented.)(Formula presented.) and (Formula presented.)(Formula presented.)are conjugate in G, then they are conjugate in (Formula presented.)(Formula presented.). The main purpose of the note was to study the meanings of this condition, as well as showing many examples of G and (Formula presented.)(Formula presented.) which do (or do not) satisfy Condition ((Formula presented.)(Formula presented.)).

Original language	English
Pages (from-to)	97-104
Number of pages	8
Journal	Japanese Journal of Mathematics
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/s11537-014-1391-7
Publication status	Published - 2015 Mar

Keywords

Gelfand pair
commutative association scheme

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s11537-014-1391-7

Cite this

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AU - Tanaka, Hajime

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N2 - 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 σsatisfy Condition ((Formula presented.)(Formula presented.)) if the following condition is satisfied: if for (Formula presented.)(Formula presented.), (Formula presented.)(Formula presented.) and (Formula presented.)(Formula presented.)are conjugate in G, then they are conjugate in (Formula presented.)(Formula presented.). The main purpose of the note was to study the meanings of this condition, as well as showing many examples of G and (Formula presented.)(Formula presented.) which do (or do not) satisfy Condition ((Formula presented.)(Formula presented.)).

AB - 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 σsatisfy Condition ((Formula presented.)(Formula presented.)) if the following condition is satisfied: if for (Formula presented.)(Formula presented.), (Formula presented.)(Formula presented.) and (Formula presented.)(Formula presented.)are conjugate in G, then they are conjugate in (Formula presented.)(Formula presented.). The main purpose of the note was to study the meanings of this condition, as well as showing many examples of G and (Formula presented.)(Formula presented.) which do (or do not) satisfy Condition ((Formula presented.)(Formula presented.)).

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KW - commutative association scheme

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Appendix: On some Gelfand pairs and commutative association schemes

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