A Hecke algebra is spanned by the double this space of the group it cor- responds to, and Gelfand pairs consist of a group and a subgroup such that the subgroup's double these commute.
A Hecke algebra is spanned by the double this space of the group it cor- responds to, and Gelfand pairs consist of a group and a subgroup such that the subgroup's double these commute. Showing that each of these has the same number of elements is crucial to the proof of   Lagrange's theorem, which guar- antees that the order of a subgroup of a group divides the order of the group. A ne subspaces of a vector space are these, and if a subgroup H is normal, then its set of left these and its set of right these will be equal. For ten points, identify these structures in group theory where a subgroup H is multiplied on either the left or the right by an element g.
A Hecke algebra is spanned by the double this space of the group it cor- responds to, and Gelfand pairs consist of a group and a subgroup such that the subgroup's double these commute.
cosets