Twisted Gelfand Pairs
A generalization of the notion of Gelfand pair is the notion of twisted Gelfand pair. Namely a pair (G,K) is called a twisted Gelfand pair with respect to the character χ of a the group K, if the Gelfand property holds true when the trivial representation is replaced with the character χ. For example in case when K is compact it meanes that the dimension of HomK(π, χ)) is less than or equal to 1. One can adapt the criterion for Gelfand pairs to the case of twisted Gelfand pairs.
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