A weighted version of quantization commutes with reduction for a toric manifold

2003/07/24 by José Agapito, Agapito, José
Mathematics · #52B20 #53D20 (Secondary) #65B15 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.CO #math.SG #msc:52B20 #msc:53D20 #msc:65B15

paper · pdf · doi:10.48550/arxiv.math/0307318

14 pages, 2 figures. Followed suggestions by referee and restructured all sections. Accepted for publication

arxiv created 2005/03/16 · arxiv updated 2009/12/01

Abstract

We compute explicitly the equivariant Hirzebruch χ_y-characteristic of an equivariant complex line bundle over a toric manifold and state a weighted version of the quantization commutes with reduction principle in symplectic geometry. Then, we give a weighted decomposition formula for any simple polytope in \Rⁿ. This formula generalizes a polytope decomposition due to Lawrence [10] and Varchenko [14] and extends a previous weighted version obtained by Karshon, Sternberg and Weitsman [9].

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