Open AccessOn Gelfand pairs associated to transitive groupoids
Author(s) -
Ibrahima Toure,
Kinvi Kangni
Publication year - 2013
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2013.33.4.751
Subject(s) - mathematics , transitive relation , haar measure , pure mathematics , hausdorff space , invariant (physics) , locally compact space , second countable space , commutative property , convolution (computer science) , countable set , combinatorics , discrete mathematics , machine learning , artificial neural network , computer science , mathematical physics
Let \(G\) be a topological locally compact, Hausdorff and second countable groupoid with a Haar system and \(K\) a compact subgroupoid of \(G\) with a Haar system too. \((G,K)\) is a Gelfand pair if the algebra of bi-\(K\)-invariant functions is commutative under convolution. In this paper, we give a characterization of Gelfand pairs associated to transitive groupoids which generalize a well-known result in the groups case. Using this result, we prove that the study of Gelfand pairs associated to transitive groupoids is equivalent to that of Gelfand pairs associated to its isotropy groups