Abstract
Let G be a reductive Lie group with compact center. A unitary representation p of G is said to be strongly L p if, for a dense set of vectors v in the space of ρ, the matrix coefficients x ↦ (ρ(x)v,v) all lie in L p(G). Let p(G) be the smallest real number such that any irreducible infinite dimensional unitary representation is strongly L p for any p > p(G). The existence of p(G) < ∞ is equivalent to Kazhdan’s “property (T)”. Indeed, the explicit determination of p(G) may be viewed as a quantitative version of Kazhdan’s property (T). In this paper we compute the numbers p(G) for the real classical groups.
Sloan Fellow. Supported in part by NSF grant No. DMS-9203142
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Li, JS. (1995). The Minimal Decay of Matrix Coefficients for Classical Groups. In: Cheng, M., Deng, Dg., Gong, S., Yang, CC. (eds) Harmonic Analysis in China. Mathematics and Its Applications, vol 327. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0141-7_8
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DOI: https://doi.org/10.1007/978-94-011-0141-7_8
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