Journal of Lie Theory, Vol. 9, No. 2, pp. 461-480 (1999)

Square-integrability of tensor products

Matthias Mayer

Zentrum Mathematik, Technische Universität München, D-80290 München,

Abstract: This paper is concerned with $C_0-$representations of locally compact groups. The focus is on the relationship between the $C_0-$property and square-integrability, the latter meaning that the representation is quasi-equivalent to a subrepresentation of the regular one. We show that for certain real algebraic groups every $C_0-$representation has a square-integrable tensor power and discuss some classes of groups enjoying this property. We point out to which extent this result supports a conjecture of Figa-Talamance and Piccardello concerning the radical of the Fourier algebra in the Fourier-Stieltjes algebra. Finally, we give a simple criterion for a $C_0-$representation to be square-integrable.

Keywords: square-integrability, real algebraic groups, $C_0-$property, $C_0-$representation

Classification (MSC91): 22D12

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