Abstract
Let G be a finite group and K ≤ G a subgroup. Recalling the equality between the induced representation \((\mathrm {Ind}^G_K\iota _K,\mathrm {Ind}^G_K{\mathbb {C}})\) and the permutation representation (λ, L(G)K), (1.11) yields a ∗-algebra isomorphism between the algebra of bi-K-invariant functions on G and the commutant of the representation obtained by inducing to G the trivial representation of K.
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Ceccherini-Silberstein, T., Scarabotti, F., Tolli, F. (2020). Hecke Algebras. In: Gelfand Triples and Their Hecke Algebras. Lecture Notes in Mathematics, vol 2267. Springer, Cham. https://doi.org/10.1007/978-3-030-51607-9_2
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DOI: https://doi.org/10.1007/978-3-030-51607-9_2
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