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

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

2003-07-24

arxiv.org/abs/math/0307318v2

Mathematics

Symplectic Geometry

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

Scientific paper

We compute explicitly the equivariant Hirzebruch $\chi_y$-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 $\R^n$. 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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