Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On localization and Riemann-Roch numbers for symplectic quotients   Suppose $(M,\omega)$ is a compact symplectic manifold acted on by a compact
Lie group $K$ in a Hamiltonian fashion, with moment map $\mu: M \to \Lie(K)^*$
and Marsden-Weinstein reduction $M_{red} = \mu^{-1}(0)/K$. In this paper, we
assume that $M$ has a $K$-invariant K\"ahler structure. In an earlier paper, we
proved a formula (the residue formula) for $\eta_0 e^{\omega_0}[M_{red}]$ for
any $\eta_0 \in H^*(M_{red})$, where $\omega_0$ is the induced symplectic form
on $M_{red}$. Here we apply the residue formula in the special case $\eta_0 =
Td(M_{red})$; when $K$ acts freely on $\mu^{-1}(0)$ this yields a formula for
the Riemann-Roch number $RR (L_{red})$ of a holomorphic line bundle $L_{red}$
on $M_{red}$ that descends from a holomorphic line bundle $L$ on $M$ for which
$c_1(L) = \omega$. Using the holomorphic Lefschetz formula we similarly obtain
a formula for the $K$-invariant Riemann-Roch number $RR^K(L) $ of $L$. In the
case when the maximal torus $T$ of $K$ has dimension one (except in a few
special circumstances), we show the two formulas are the same. Thus in this
special case the residue formula is equivalent to the result of Guillemin and
Sternberg that $RR(L_{red}) = RR^K(L)$. (The residue formula was proved under
the assumption that 0 is a regular value of $\mu$, and was given in terms of
the restrictions of classes in the equivariant cohomology $H^*_T(M) $ of $M$ to
the

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: cs