Related papers: Representation of small conformal algebra
An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the positive kernel $|K_{(i\tau+\alpha)/2}(x)|^2, \alpha \ge 0,\ x…
We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some…
Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…
It is shown explicitly that the correlation functions of Conformal Field Theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of $\W_\infty$-algebra. This algebra is constructed…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra $F"_4$ which is the split rank one form of the exceptional Lie algebra…
We construct a topology on the standard Hilbert module $l^2(\mathcal A)$ over a unital $W^*$-algebra $\mathcal A$ such that any "compact" operator, (i.e.\ any operator in the norm closure of the linear span of the operators of the form…
We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of…
In this paper, we generalize the fractional order difference operator using $l$- Pochhammer symbol and define $l$- fractional difference operator. The $l$- fractional difference operator is further used to introduce a class of difference…
The isomorphism between the reduction algebra and the invariant differential operators on G/H is sketched.
Theory of differential operators on associative algebras is not extended to the non-associative ones in a straightforward way. We consider differential operators on Lie algebras. A key point is that multiplication in a Lie algebra is its…
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
A general concept of a Hausdorff-type operator that absorbs all types of operators bearing the name `` Hausdorff operator'' and many others is considered. The characteristic features of this concept are the consideration of kernels…
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the…
Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.
A classification of weakly compact multiplication operators on L(L_p), $1<p<\infty$, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of $\ell_p$-strictly singular operators, and…
We define left and right kernels of representations of Hopf algebras. In the case of group algebras, left and right kernels coincide and they are the usual kernels of modules. In the general case we show that these kernels coincide with the…
A unital $C^*$-algebra is called $N$-subhomogeneous if its irreducible representations are finite dimensional with dimension at most $N$. We extend this notion to operator systems, replacing irreducible representations by boundary…
In this paper we define an integral operator on Lp and obtain its degree of convergence in the appropriate norm. By specializing the kernel of the integral operator we obtain many known results as corollaries. We have also applied our…
For each $S \in L(E)$ (with $E$ a Banach space) the operator $R(S) \in L(E^{**}/E)$ is defined by $R(S)(x^{**}+E) = S^{**}x^{**}+E$ \quad ($x^{**}\in E^{**}$). We study mapping properties of the correspondence $S\to R(S),$ which provides a…
In earlier work, Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the…