Abstract
Let K be a closed Lie subgroup of the unitary group U(n) acting by automorphisms on the (2n+1)-dimensional Heisenberg group $H_n$. We say that $(K,H_n)$ is a Gelfand pair when the set $L^1_K(H_n)$ of integrable K-invariant functions on $H_n$ is an abelian
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