On Martin Bordemann's proof of the existence of projectively equivariant quantizations

Pierre Lecomte

Displaying similar documents to “On Martin Bordemann's proof of the existence of projectively equivariant quantizations”

Conformally equivariant quantization : existence and uniqueness

Christian Duval, Pierre Lecomte, Valentin Ovsienko (1999)

Annales de l'institut Fourier

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We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-riemannian manifold $(M, g)$ . In other words, we establish a canonical isomorphism between the spaces of polynomials on $T^{*} M$ and of differential operators on tensor densities over $M$ , both viewed as modules over the Lie algebra $o (p + 1, q + 1)$ where $p + q = dim (M)$ . This quantization exists for generic values of the weights of the tensor densities and we compute the critical values of the...

Higher order valued reduction theorems for classical connections

Josef Janyška (2005)

Open Mathematics

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We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.

On equivariant maps between Stiefel manifolds.

Petrović, Zoran Z. (1997)

Publications de l'Institut Mathématique. Nouvelle Série

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Second-order conformally equivariant quantization in dimension $1 | 2$ .

Mellouli, Najla (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Equivariant differential operators

Reimann, H. M.

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This paper contains the lectures given by the author at the Winter School on “Geometry and Physics” in Srní 2001. These lectures are based on two recent works of the author with A. Korányi and on a forthcoming paper with K. Johnson and A. Korányi. In the paper results are presented concerning equivariant differential operators on homogeneous spaces (section 1), first order equivariant differential operators on boundaries of symmetric spaces (section 2), the Poisson transform (section...

Brouwer degree, equivariant maps and tensor powers.

Balanov, Z., Krawcewicz, W., Kushkuley, A. (1998)

Abstract and Applied Analysis

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On equivariant deformations of maps.

Antonio Vidal (1988)

Publicacions Matemàtiques

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We work in the smooth category: manifolds and maps are meant to be smooth. Let G be a finite group acting on a connected closed manifold X and f an equivariant self-map on X with f_|A fixpointfree, where A is a closed invariant submanifold of X with codim A ≥ 3. The purpose of this paper is to give a proof using obstruction theory of the following fact: If X is simply connected and the action of G on X - A is free, then f is equivariantly deformable rel. A to fixed...

Schwarzian derivative related to modules of differential operators on a locally projective manifold

S. Bouarroudj, V. Ovsienko (2000)

Banach Center Publications

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We introduce a 1-cocycle on the group of diffeomorphisms Diff(M) of a smooth manifold M endowed with a projective connection. This cocycle represents a nontrivial cohomology class of Diff(M) related to the Diff(M)-modules of second order linear differential operators on M. In the one-dimensional case, this cocycle coincides with the Schwarzian derivative, while, in the multi-dimensional case, it represents its natural and new generalization. This work is a continuation of [3] where the...