Related papers: Finite-dimensional representations of the elliptic…

We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a…

The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of…

The potential of the $A_2$ quantum elliptic model (3-body Calogero-Moser elliptic model) is defined by the pairwise three-body interaction through Weierstrass $\wp$-function and has a single coupling constant. A change of variables has been…

We propose a new construction of vertex operators of the elliptic quantum toroidal algebra $U_{t_1,t_2,p}(\mathfrak{gl}_{N,tor})$ by combining representations of the algebra and formulas of the elliptic stable envelopes for the…

We show that each unitary representation of the N=2 superVirasoro algebra can be realized in terms of ``collective excitations'' over a filled Dirac sea of fermionic operators satisfying a generalized exclusion principle. These are…

Let $(\overline M,\overline g)$ be a time- and space-oriented Lorentzian spin manifold, and let $M$ be a compact spacelike hypersurface of $\overline M$ with induced Riemannian metric $g$ and second fundamental form $K$. If $(\overline…

In this paper we prove a formula that relates M\"uger's centralizer in the category of representations of a factorizable Hopf algebra to the notion of Hopf kernel of a representation of the dual Hopf algebra. Using this relation we obtain a…

Let $\Omega \subset \mathbb{R}^N$ ($N \geq 3$) be a $C^2$ bounded domain and $K \subset \Omega$ be a compact, $C^2$ submanifold in $\mathbb{R}^N$ without boundary, of dimension $k$ with $0\leq k < N-2$. We consider the Schr\"odinger…

We obtain a complete characterization of the entire functions $g$ such that the integral operator $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ is bounded or compact, on a large class of Fock spaces $\mathcal{F}^\phi_p$, induced by…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$…

This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…

Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V^G-modules which occur as submodules of irreducible V-modules by using intertwining operators for…

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and $M$ be the total space of a principal bundle $G\to M\to X$ so that $M$ is also a strongly pseudoconvex complex manifold. In this work, we show that if $G$ acts by…

Let $\X\simeq G/K$ be a Riemannian symmetric space of non-compact type, $\widetilde \X$ its Oshima compactification, and $(\pi,\mathrm{C}(\widetilde \X))$ the regular representation of $G$ on $\widetilde \X$. We study integral operators on…

Let $n\ge 1$ and $\mathfrak{T}_{m}$ be the bilinear square Fourier multiplier operator associated with a symbol $m$, which is defined by $$ \mathfrak{T}_{m}(f_1,f_2)(x) = \biggl( \int_{0}^\infty\Big|\int_{(\mathbb{R}^n)^2} e^{2\pi ix\cdot…

In the present paper we construct explicitly the intertwining differential operators for the Jacobi algebra ${\cal G}_2.$ For the construction we use the singular vectors of the Verma modules over ${\cal G}_2$ which we have constructed…

Lagrangian constraints of the spin 2 selfdual theory in a 2+1 flat space-time are studied and the one degree of freedom reduced action is obtained. From this formulation, the quantum operator algebra is computed and the spin contribution on…

It is shown that, under some natural additional conditions, an operator which intertwines one cyclic singular unitary operator with one dimensional perturbation of another cyclic singular unitary operator is the operator of multiplication…

Let $G$ be the identity component of the isometry group for an arbitrary curved two-point homogeneous space $M$. We consider algebras of $G$-invariant differential operators on bundles of unit spheres over $M$. The generators of this…

The bilinear maximal operator defined below maps $L^p\times L^q$ into $L^r$ provided $1<p,q<\zI$, $1/p+1/q=1/r$ and $2/3<r\le1$. $$ Mfg(x)=\sup_{t>0}\frac1{2t}\int_{-t}^t\abs{f(x+y)g(x-y)} dy.$$ In particular $Mfg$ is integrable\thinspace…