Quantification de certains espaces hermitiens symétriques
Quantification d'une variété symplectique
Quantification et approximations semi-classiques
Quantification formelle des variétés de Poisson
Quantification géométrique et réduction symplectique
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...
Quantization and global properties of manifolds
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 a dimensionally reduced Seiberg-Witten moduli space.
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...
Quantization of Poisson Hamiltonian systems
In this paper we recall the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group theories.
Quantization of Poisson structures on .
Quantization of the cotangent bundle via the tangent groupoid
Quantization on submanifolds
Quantum 4-sphere: the infinitesimal approach
We describe how the constructions of quantum homogeneous spaces using infinitesimal invariance and quantum coisotropic subgroups are related. As an example we recover the quantum 4-sphere of [2] through infinitesimal invariance with respect to .
Quantum Cohomology and Crepant Resolutions: A Conjecture
We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold to the quantum cohomology of a crepant resolution of . We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines higher-genus...
Quantum cohomology and its application.
Quantum Cohomology and Periods
In a previous paper, the author introduced an integral structure in quantum cohomology defined by the -theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle to the previous results, we find an explicit relationship between solutions to the quantum differential equation of toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism of...
Quantum cohomology of flag manifolds and quantum Toda lattices.
Quantum deformations of the Lorentz group. The Hopf-algebra level