TY - JOUR
T1 - Appendix
T2 - On some Gelfand pairs and commutative association schemes
AU - Bannai, Eiichi
AU - Tanaka, Hajime
N1 - Publisher Copyright:
© 2014, The Mathematical Society of Japan and Springer Japan.
PY - 2015/3
Y1 - 2015/3
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.)).
KW - Gelfand pair
KW - commutative association scheme
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U2 - 10.1007/s11537-014-1391-7
DO - 10.1007/s11537-014-1391-7
M3 - Article
AN - SCOPUS:84924777554
VL - 10
SP - 97
EP - 104
JO - Japanese Journal of Mathematics
JF - Japanese Journal of Mathematics
SN - 0289-2316
IS - 1
ER -