TY  - JOUR
ID  - Toure2013
LB  - Toure2013
AU  - Toure, Ibrahima
AU  - Kangni, Kinvi
TI  - On Gelfand pairs associated to transitive groupoids
ST  - On Gelfand pairs associated to transitive groupoids
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 4
SP  - 751
EP  - 762
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.4.751
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.4.751
AB  - 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.
KW  - transitive groupoids
KW  - groupoid representation
KW  - Gelfand pairs
SN  - 1232-9274
ER  -