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Representations of current groups
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additive family analysis application assume called commutator compact second countable completes the proof complex numbers complex valued function conditionally positive definite connected Consider contains continuous function continuous normalised continuous tensor product defined denote dimensional Edited element equation exists extended finite follows function on G Further group acting Hence Hilbert space holds identity implies induced infinitely divisible invariant conditionally positive invariant positive definite kernels on XxX Lemma Let G limit locally compact second measure multiplicative neighbourhood normalised positive definite Note obtain operator origin positive definite function positive definite kernels Probability projective representation properties proved Remark representation of G respectively result satisfying second countable group second order cocycle sequence space H spanned standard borel space subgroup subnet Suppose takes Theorem Theory uniformly infinitesimal family unitary representation vectors write x,yex