Functional Calculus And Coadjoint Orbits von Raed Raffoul (2009, Taschenbuch) online kaufen

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The Kirillov character formula gives a strikingcorrespondence between the unitary irreduciblerepresentations of a compact semisimple Lie group andits set of integral orbits on the dual of its Liealgebra. In this thesis, the same correspondence isderived without the use of character theory. It isshown to be related to the convexity properties ofthe support of the Weyl functional calculus of theinfinitesimal generators of the representation. Thisresult uses Edward Nelson's theory of "operants" in afundamental way. This hadbeen developed to put Feynman's operator calculus ona rigorous basis. In particular, a beautiful explicitformula of Nelson for the Weyl calculus facilitatesthe extension of the Kirillov formula to the matrixcoefficients of the representation, thus giving a"non-commutative" Kirillov-type formula for compactLie groups.