-analog of Gelfand-Graev basis for the noncompact quantum algebra .
-boson in quantum integrable systems.
-deformation of the Virasoro algebra and lattice conformal theories
-deformed bi-local fields. II.
-Wakimoto modules and integral formulae of solutions of the quantum Knizhnik-Zamolodchikov equations.
Quadratic algebra approach to an exactly solvable position-dependent mass Schrödinger equation in two dimensions.
Quadratic and homogeneous Hamilton-Poisson systems on .
Quadratic homogeneous ODE systems of Jordan-rigid body type.
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...
Quantised -differential algebras
We propose a definition of a quantised -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of are natural examples of such algebras.
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 cohomology in semi-simple Lie algebras.
Quantization of Drinfeld Zastava in type
Drinfeld Zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of the affine Lie algebra . We introduce an affine, reduced, irreducible, normal quiver variety which maps to the Zastava space bijectively at the level of complex points. The natural Poisson structure on the Zastava space can be described on in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian...
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 semisimple real Lie groups
We provide a novel construction of quantized universal enveloping -algebras of real semisimple Lie algebras, based on Letzter’s theory of quantum symmetric pairs. We show that these structures can be ‘integrated’, leading to a quantization of the group C-algebra of an arbitrary semisimple algebraic real Lie group.
Quantizations of braided derivations. I: Monoidal categories.
Quantizations of braided derivations. II: Graded modules.
Quantizations of braided derivations. III: Modules with action by a group.
Quantized semisimple Lie groups
The goal of this expository paper is to give a quick introduction to -deformations of semisimple Lie groups. We discuss principally the rank one examples of , , and related algebras. We treat quantized enveloping algebras, representations of , generalities on Hopf algebras and quantum groups, -structures, quantized algebras of functions on -deformed compact semisimple groups, the Peter-Weyl theorem, -Hopf algebras associated to complex semisimple Lie groups and the Drinfeld double, representations...