2005/02/09 by A. A. Bytsenko, Bytsenko, A. A., M. Libine +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Symplectic Geometry (math.SG) #hep-th #math.AG #math.SG
paper · pdf · doi:10.48550/arxiv.math/0502190
30 pages, 4 figures
arxiv created 2005/02/11 · arxiv updated 2009/12/01
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.