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.
Read more about this topic: Gelfand Pair
Famous quotes containing the word twisted:
“One of the great natural phenomena is the way in which a tube of toothpaste suddenly empties itself when it hears that you are planning a trip, so that when you come to pack it is just a twisted shell of its former self, with not even a cubic millimeter left to be squeezed out.”
—Robert Benchley (1889–1945)