In the field of harmonic analysis and representation theory, a **Gelfand pair** is a specific type of mathematical structure that arises when studying the representations of groups. More concretely, a Gelfand pair consists of a pair of groups (typically a group \( G \) and a subgroup \( H \)) such that the algebra of \( H \)-invariant functions on \( G \) is particularly "nice" for some representation theory considerations.
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