Algebras of invariant functions on the Šilov boundary of generalized half-planes

Carcano, Giovanna

doi:10.1090/S0002-9939-1991-1039253-2

Algebras of invariant functions on the Šilov boundary of generalized half-planes
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by Giovanna Carcano PDF

Proc. Amer. Math. Soc. 111 (1991), 743-753 Request permission

Abstract:

Let $\mathcal {N}$ be the nilpotent Lie group identified to the Šilov boundary of a symmetric generalized half-plane $\mathcal {D}$ and $L$ a compact group acting on $\mathcal {N}$ by automorphisms, arising from the realization of $\mathcal {D}$ as hermitian symmetric space. Is then $(L \ltimes \mathcal {N},L)$ a Gelfand pair? We study the problem and resolve it in the case of classical families.

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