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- W2024894435 abstract "LetSbe a connected and simply connected unimodular solvable Lie group andKa connected compact Lie group acting onSas automorphisms. We call the pair (K S) a Gelfand pair if the Banach ∗-algebraL1K(S) of allK-invariant integrable functions onSis a commutative algebra. In this paper we give a necessary and sufficient condition for the pair (K; S) to be a Gelfand pair using the representation theory of non-type-I solvable Lie groups. For a Gelfand pair (K; S) we realize all irreducibleK-spherical representations ofK⋉Sfrom irreducible unitary representations ofS." @default.
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- W2024894435 date "1998-12-01" @default.
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- W2024894435 title "Remarks on Gelfand Pairs Associated to Non-Type-I Solvable Lie Groups" @default.
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- W2024894435 doi "https://doi.org/10.1006/jfan.1998.3350" @default.
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