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Quantification pour les paires symétriques et diagrammes de Kontsevich

Alberto S. Cattaneo, Charles Torossian (2008)

Annales scientifiques de l'École Normale Supérieure

In this article we use the expansion for biquantization described in [7] for the case of symmetric spaces. We introduce a function of two variables E ( X , Y ) for any symmetric pairs. This function has an expansion in terms of Kontsevich’s diagrams. We recover most of the known results though in a more systematic way by using some elementary properties of this E function. We prove that Cattaneo and Felder’s star product coincides with Rouvière’s for any symmetric pairs. We generalize some of Lichnerowicz’s...

Quantitative spectral gap for thin groups of hyperbolic isometries

Michael Magee (2015)

Journal of the European Mathematical Society

Let Λ be a subgroup of an arithmetic lattice in SO ( n + 1 , 1 ) . The quotient n + 1 / Λ has a natural family of congruence covers corresponding to ideals in a ring of integers. We establish a super-strong approximation result for Zariski-dense Λ with some additional regularity and thickness properties. Concretely, this asserts a quantitative spectral gap for the Laplacian operators on the congruence covers. This generalizes results of Sarnak and Xue (1991) and Gamburd (2002).

Quantization of pencils with a gl-type Poisson center and braided geometry

Dimitri Gurevich, Pavel Saponov (2011)

Banach Center Publications

We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and...

Quantizations and symbolic calculus over the p -adic numbers

Shai Haran (1993)

Annales de l'institut Fourier

We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the p -adic numbers. We apply this theory to the study of elliptic operators over the p -adic numbers and determine their asymptotic spectral behavior.

Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras.

Karin Baur, Anne Moreau (2011)

Annales de l’institut Fourier

We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements. Parabolic subalgebras of a semisimple Lie algebra are not always quasi-reductive (except in types A or C by work of Panyushev). The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo,...

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