Authors: Voit, Michael
Title: Generalized commutative association schemes, hypergroups, and positive product formulas
Language (ISO): en
Abstract: It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. In this paper we present several discrete generalizations of association schemes which also lead to associated hypergroups. We show that discrete commutative hypergroups associated with such generalized association schemes admit dual positive convolutions at least on the support of the Plancherel measure. We hope that examples for this theory will lead to the existence of new dual positive product formulas in near future.
Subject Headings: Association schemes
Gelfand pairs
Hecke pairs
spherical functions
positive product formulas
dual convolution
distance-transitive graphs.
Issue Date: 2016-08
Appears in Collections:Preprints der Fakultät für Mathematik

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