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...
Quantum Affine Algebras and Deformations of the Virasoro and -Algebras
Quantum affine algebras, combinatorics of Young walls, and global bases.
Quantum (Co)Modules for Dual Quantum Groups
Quantum curve in -oscillator model.
Quantum deformations and superintegrable motions on spaces with variable curvature.
Quantum deformations of the Lorentz group. The Hopf-algebra level
Quantum dynamics on the worldvolume from classical cohomology.
Quantum Fibre Bundles. An Introduction
An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.
Quantum fields on noncommutative spacetimes: theory and phenomenology.
Quantum groups in higher genus and Drinfeld’s new realizations method ( case)