相关论文: Quantum Strata of Coadjoint Orbits

We encapsulate the basic notions of the theory of vertex algebras into the construction of a comonad on an appropriate category of formal distributions. Vertex algebras are recovered as coalgebras over this comonad.

The purpose of this paper is to apply deformation quantization to the study of the coadjoint orbit method in the case of real reductive groups. We first prove some general results on the existence of equivariant deformation quantization of…

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

The rational cohomology of a coadjoint orbit ${\cal O}$ is expressed as tensor product of the cohomology of other coadjoint orbits ${\cal O}_k$, with $ \hbox{dim} {\cal O}_k< \hbox{dim} {\cal O}$.

Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.

In this article, we study adjoint orbits of the Jacobi group, and in particular describe nilpotent orbits explicitely.

The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…

Quasi-elliptic cohomology is a variant of elliptic cohomology theories. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. Thus, the constructions…

We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…

We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.

The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper proves self-adjointness of these second-order elliptic operators.

We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…

We study alternating strand diagrams on the disk with an orbifold point. These are quotients by rotation of Postnikov diagrams on the disk, and we call them orbifold diagrams. We associate a quiver with potential to each orbifold diagram,…

We study coadjoint orbitopes, i.e. convex hulls of coadjoint orbits of a compact Lie group. We show that all the faces of such an orbitope are exposed. The face structure is studied by means of the momentum map and it is shown that every…

Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough…

In our previous paper, we constructed an explicit GL(n)-equivariant quantization of the Kirillov--Kostant-Souriau bracket on a semisimple coadjoint orbit. In the present paper, we realize that quantization as a subalgebra of endomorphisms…

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…

The operation of tensor product of Cohomological Field Theories (or algebras over genus zero moduli operad) introduced in an earlier paper by the authors is described in full detail, and the proof of a theorem on additive relations between…

We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological induction for quantum groups.

We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow…