Quantification géométrique : théorie et exemples
Quantification of coadjoint orbits and the theory of contractions. (Quantification d'orbites coadjointes et théorie des contractions.)
Quantification pour les paires symétriques et diagrammes de Kontsevich
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 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 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 analysis of the Satake parameters of GL₂ representations with prescribed local representations
We investigate the vertical version of the Sato-Tate conjecture for some GL₂ automorphic representations over totally real fields with specified local components at a finite set of finite places.
Quantitative spectral gap for thin groups of hyperbolic isometries
Let be a subgroup of an arithmetic lattice in . The quotient 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 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 and irreducible representations of infinite-dimensional transformation groups and Lie algebras.
Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series
In this paper we show that the multiplicities of holomorphic discrete series representations relative to reductive subgroups satisfy the credo “quantization commutes with reduction”.
Quantization of pencils with a gl-type Poisson center and braided geometry
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 -adic numbers
We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the -adic numbers. We apply this theory to the study of elliptic operators over the -adic numbers and determine their asymptotic spectral behavior.
Quantum co-adjoint orbits of the group of affine transformations of the complex line.
Quantum deformations of the Lorentz group. The Hopf-algebra level
Quantum half-planes via deformation quantization.
Quantum Racah coefficients and subrepresentation semirings.
Quantum faithfully detects mapping class groups modulo center.
Quasi-bigèbres jacobiennes
Quasicrystallographic groups on Minkowski spaces.
Quasi-exactly solvable Schrödinger operators in three dimensions.
Quasiflats with holes in reductive groups.
Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras.
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,...
Quaternion quantum theory as a description of tachyons and the symmetry breaking