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OPERATOR KERNELS FOR IRREDUCIBLE REPRESENTATIONS OF EXPONENTIAL LIE GROUPS
Published online by Cambridge University Press: 01 October 2008
Abstract
A nine-dimensional exponential Lie group G and a linear form ℓ on the Lie algebra of G are presented such that for all Pukanszky polarizations 𝔭 at ℓ the canonically associated unitary representation ρ=ρ(ℓ,𝔭) of G has the property that ρ(ℒ1(G)) does not contain any nonzero operator given by a compactly supported kernel function. This example shows that one of Leptin’s results is wrong, and it cannot be repaired.
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- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 301 - 316
- Copyright
- Copyright © 2008 Australian Mathematical Society