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Toeplitz operators and Hamiltonian torus action
This paper is devoted to semi-classical aspects of symplectic reduction.
Consider a compact prequantizable Kahler manifold M with a Hamiltonian torus
action. Guillemin and Sternberg introduced an isomorphism between the invariant
part of the quantum space associated to M and the quantum space associated to
the symplectic quotient of M, provided this quotient is non-singular.
We prove that this isomorphism is a Fourier integral operator and that the
Toeplitz operators of M descend to Toeplitz operators of the reduced phase
space. We also extend these results to the case where the symplectic quotient
is an orbifold and estimate the spectral density of a reduced Toeplitz
operator, a result related to the Riemann-Roch-Kawazaki theorem.Comment: corrected typos, accepted for publication in J. Funct. Ana
A new species of Platyauchenia Stürm, 1843 (Coleoptera: Chrysomelidae: Cassidinae) from Brazil
The genus Platyauchenia Stürm, 1843 is reviewed. Platyauchenia quinquemaculata Pic, 1921 is a synonym of P. latreillei (Castelnau 1840), new synonymy. Platyauchenia ruficollis new species is described from Brazil. Each species is illustrated and a key to the species is provided
A new species of Cephaloleia Chevrolat, 1837 (Coleoptera: Chrysomelidae: Cassidinae) from Dominica
A new species of Cephaloleia, C. simplex from Dominica, is described and illustrated. The species of Cephaloleia known from the Caribbean are reviewed and a key to those species is presented
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