OPERATOR KERNELS FOR IRREDUCIBLE REPRESENTATIONS OF EXPONENTIAL LIE GROUPS

Poguntke D. OPERATOR KERNELS FOR IRREDUCIBLE REPRESENTATIONS OF EXPONENTIAL LIE GROUPS. Bulletin of the Australian Mathematical Society. 2008;78(2):301-316.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 rho = rho(l, p) of G has the property that rho(L-1(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