相关论文: Duality for Knizhnik-Zamolodchikov and Dynamical O…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
The aim of this paper is to introduce a Dunkl generalization of the operators including two variable Hermite polynomials which are defined by Krech [14](Krech, G. A note on some positive linear operators associated with the Hermite…
We explore differential operators, $T$, that diagonalize on a simple basis, $\{B_n(x)\}_{n=0}^\infty$, with respect to some sequence of real numbers, $\{a_n\}_{n=0}^\infty$, and sequence of polynomials, $\{Q_k(x)\}_{k=0}^\infty$, as in $…
We discuss some of the analytic properties of lens space indices for 4d N=2 theories of class S. The S-duality properties of these theories highly constrain the lens space indices, and imply in particular that they are naturally acted upon…
We generalize our picture in [arXiv:0904.1744], and consider a pure abelian gauge theory on a four-manifold with nonlocal operators of every codimension arbitrarily and simultaneously inserted. We explicitly show that (i) the theory enjoys…
On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides…
The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant…
We consider non-selfadjoint operator algebras $\mathfrak{L}(G,\lambda)$ generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs $G$. These algebras may be viewed as noncommutative generalizations of…
In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as…
We point out that fermionic unitary operators which anticommute among themselves appear in various situations in quantum field theories with anomalies in the Hamiltonian formalism. To illustrate, we give multiple derivations of the fact…
If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object $G^{\vee}$. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
We formulate a general super duality conjecture on connections between parabolic categories O of modules over Lie superalgebras and Lie algebras of type A, based on a Fock space formalism of their Kazhdan-Lusztig theories which was…
We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov's first and second Poincare duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz…
We discuss structural similarities between Knizhnik--Zamolodchikov equations (in fact, their simplest version needed to introduce the Drinfeld associator) and Dyson--Schwinger equations. We emphasize that the latter allow for a filtration…
Following the definitions of the algebras of differential operators, $\beta$-differential operators, and the quantum differential operators on a noncommutative (graded) algebra given in \cite{LR}, we describe these operators on the free…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
Over the $(1,n)$-dimensional real supercircle, we consider the $\mathcal{K}(n)$-modules of linear differential operators, $\frak{D}^n_{\lambda,\mu}$, acting on the superspaces of weighted densities, where $\mathcal{K}(n)$ is the Lie…
The structure of S-duality in U(1) gauge theory on a 4-manifold M is examined using the formalism of noncommutative geometry. A noncommutative space is constructed from the algebra of Wilson-'t Hooft line operators which encodes both the…