Let N be the nilpotent Lie group identified to the Silov boundary of a symmetric generalized half-plane D and L a compact group acting on N by automorphisms, aris ng from the realization of D as hermitian symmetric space. Is then (L⋊ N, L) a Gelfand pair? We study the problem and resolve it in the case of classical families
Carcano, G. (1991). Algebras of inveriant functions on the silov boundary of generalized half-planes. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 111(3), 743-753 [10.1090/S0002-9939-1991-1039253-2].
Algebras of inveriant functions on the silov boundary of generalized half-planes
CARCANO, GIOVANNA
1991
Abstract
Let N be the nilpotent Lie group identified to the Silov boundary of a symmetric generalized half-plane D and L a compact group acting on N by automorphisms, aris ng from the realization of D as hermitian symmetric space. Is then (L⋊ N, L) a Gelfand pair? We study the problem and resolve it in the case of classical families
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