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A Duistermaat-Heckman formula for admissible coadjoint orbits. (English) Zbl 0920.22009

Doebner, H.-D. (ed.) et al., Lie theory and its applications in physics. Proceedings of the international workshop, Clausthal, Germany, August 14–17, 1995. Singapore: World Scientific. 15-35 (1996).
The author obtains a general formula for admissible coadjoint orbits which specializes to: 1) the Duistermaat-Heckman formula in the case of compact Lie algebras (this formula has been obtained by Harish-Chandra), 2) the Prato-Wu formula for strictly admissible coadjoint orbits for hermitian simple Lie algebras, 3) a well-known formula for the Fourier transform of Gauss kernels for the Lie algebra \(g=h_n {{{\triangleright} {< }}} sp(n, \mathbb R)\), where \(h_n\) is the \((2n+1)\)-dimensional Heisenberg algebra, 4) a character formula of Khalgui-Kirillov-Rossmann type for those unitary highest weight representations of the group which are square integrable modulo the center and even for those singular representations which arise as holomorphically induced representations.
For the entire collection see [Zbl 0906.00015].
Reviewer: A.K.Guts (Omsk)

MSC:

22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
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