We prove a Duistermaat-Heckman type formula in a suitable non-compact setting. We use this formula to evaluate explicitly the pushforward of the Liouville measure via the moment map of both an abelian and a non-abelian group action. As an application we obtain continuous versions of well-known multiplicity formulas for the holomorphic discrete series representations.
Duistermaat-Heckman measures in a non-compact setting / E. Prato; S. Wu. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - STAMPA. - 94:(1994), pp. 113-128.
Duistermaat-Heckman measures in a non-compact setting
PRATO, ELISA
;
1994
Abstract
We prove a Duistermaat-Heckman type formula in a suitable non-compact setting. We use this formula to evaluate explicitly the pushforward of the Liouville measure via the moment map of both an abelian and a non-abelian group action. As an application we obtain continuous versions of well-known multiplicity formulas for the holomorphic discrete series representations.
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