منابع مشابه
Connected Lie Groups and Property Rd
For a locally compact group, the property of rapid decay (property RD) gives a control on the convolutor norm of any compactly supported function in terms of its L2-norm and the diameter of its support. We characterize the Lie groups that have property RD. 0. Introduction The property of rapid decay (property RD) emerged from the work of U. Haagerup in [15] and was first studied systematically ...
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We give a short elementary proof of the fact that connected semisimple real Lie groups satisfy property RD. The proof is based on a process of linearization.
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We apply V. Lafforgue’s techniques to establish property (RD) for cocompact lattices in a finite product of rank one Lie groups with Lie groups whose restricted root system is of type A2. We recall that a length function on a discrete group Γ is a function l : Γ → R+ such that the neutral element is mapped to zero, and such that l(γ) = l(γ), l(γμ) ≤ l(γ) + l(μ) for any γ, μ ∈ Γ. A discrete grou...
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We introduce concepts of intermediate rank for countable groups that “interpolate” between consecutive values of the classical (integer-valued) rank. Various classes of groups are proved to have intermediate rank behaviors. We are especially interested in interpolation between rank 1 and rank 2. For instance, we construct groups “of rank 7 4 ”. Our setting is essentially that of non positively ...
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We determine for each of the simple, simply connected, compact and complex Lie groups SU(n), Spin(4n+2) and E6 that particular region inside the unit disk in the complex plane which is filled by their mean eigenvalues. We give analytical parameterizations for the boundary curves of these so-called trace figures. The area enclosed by a trace figure turns out to be a rational multiple of π in eac...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2007
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-07-13733-5