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Ellipticity of the symplectic twistor complex

Svatopluk Krýsl (2011)

Archivum Mathematicum

For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the symplectic...

Equivariant deformation quantization for the cotangent bundle of a flag manifold

Ranee Brylinski (2002)

Annales de l’institut Fourier

Let X be a (generalized) flag manifold of a complex semisimple Lie group G . We investigate the problem of constructing a graded star product on = R ( T X ) which corresponds to a G -equivariant quantization of symbols into twisted differential operators acting on half-forms on X . We construct, when is generated by the momentum functions μ x for G , a preferred choice of where μ x φ has the form μ x φ + 1 2 { μ x , φ } t + Λ x ( φ ) t 2 . Here Λ x are operators on . In the known examples, Λ x ( x 0 ) is not a differential operator, and so the star product μ x φ ...

Explicit Kazhdan constants for representations of semisimple and arithmetic groups

Yehuda Shalom (2000)

Annales de l'institut Fourier

Consider a simple non-compact algebraic group, over any locally compact non-discrete field, which has Kazhdan’s property ( T ) . For any such group, G , we present a Kazhdan set of two elements, and compute its best Kazhdan constant. Then, settling a question raised by Serre and by de la Harpe and Valette, explicit Kazhdan constants for every lattice Γ in G are obtained, for a “geometric” generating set of the form Γ B r , where B r G is a ball of radius r , and the dependence of r on Γ is described explicitly....

Exponents in Archimedean Arthur packets

Nicolas Bergeron, Laurent Clozel (2013)

Annales de l’institut Fourier

Generalizing the proof – by Hecht and Schmid – of Osborne’s conjecture we prove an Archimedean (and weaker) version of a theorem of Colette Moeglin. The result we obtain is a precise Archimedean version of the general principle – stated by the second author – according to which a local Arthur packet contains the corresponding local L -packet and representations which are more tempered.

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