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