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2005•Journal of Dynamical Systems and Geometric TheoriesRequires access

Localization of Equivariant Cohomology for Compact and Non-Compact Group Actions

A. A. Bytsenko, Matvei Libine, Floyd L. Williams

Open publisher page 4 citations

Abstract

We give a brief introduction to the Berline-Vergne localization formula for the finite-dimensional setting and indicate how the Duistermaat-Heckman formula is derived from it. We consider applications of the localization formula when it is specialized to a maximal dimensional co-adjoint orbit. In particular, the case when the co-adjoint orbit is a quotient G/T of a connected Lie group G modulo a maximal torus T is analyzed in detail. We describe also a generalization of the localization formula to non-compact group actions.

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What this paper is about

We give a brief introduction to the Berline-Vergne localization formula for the finite-dimensional setting and indicate how the Duistermaat-Heckman formula is derived from it. We consider applications of the localization formula when it is specialized to a maximal dimensional co-adjoint orbit. In particular, the case when the co-adjoint orbit is a quotient G/T of a connected Lie group G modulo a maximal torus T is analyzed in detail. We describe also a generalization of the localization formula to non-compact group actions.

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Available abstract

We give a brief introduction to the Berline-Vergne localization formula for the finite-dimensional setting and indicate how the Duistermaat-Heckman formula is derived from it. We consider applications of the localization formula when it is specialized to a maximal dimensional co-adjoint orbit. In particular, the case when the co-adjoint orbit is a quotient G/T of a connected Lie group G modulo a maximal torus T is analyzed in detail. We describe also a generalization of the localization formula to non-compact group actions.

Key concepts: Maximal torus, Lie group, Equivariant map, Mathematics, Quotient, Modulo, Orbit (dynamics), Torus

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