Related papers: Construction of Intertwining Operators between Hol…

We study intertwining relations for $n\times n$ matrix non-Hermitian, in general, one-dimensional Hamiltonians by $n\times n$ matrix linear differential operators with nondegenerate coefficients at $d/dx$ in the highest degree. Some methods…

In this paper we study the problem of explicitly describing the space of invariant linear forms on induced distinguished representations in terms of invariant linear forms on the inducing representation. More precisely, for certain tempered…

The intertwining operator constructed in [Sz1,Sz2] does not appear in the right form. It is established there by using only the anticommutators. The correct operator must involve all endomorphisms, which are unified by the Z-Fourier…

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra $G_{2(2)}$. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We…

Consider a reductive group G over a non-archimedean local field. The Galois group Gal(C/Q) acts naturally on the category of smooth complex G-representations. We prove that this action stabilizes the class of standard modules. This…

In this paper we prove holomorphy for certain intertwining operators arising from the theory of Eisenstein series.

For a simple real Lie group $G$ with Heisenberg parabolic subgroup $P$, we study the corresponding degenerate principal series representations. For a certain induction parameter the kernel of the conformally invariant system of second order…

There is a commutative algebra of differential-difference operators, acting on polynomials on R_2, associated with the reflection group B2. This paper presents an integral transform which intertwines this algebra, allowing one free…

In this article we study differential symmetry breaking operators between principal series representations induced from minimal parabolic subgroups for the pair $(\operatorname{GL}_{n+1}(\mathbb{R}),\operatorname{GL}_n(\mathbb{R}))$. Using…

A real reductive pair $(G,H)$ is called strongly spherical if the homogeneous space $(G\times H)/{\rm diag}(H)$ is real spherical. This geometric condition is equivalent to the representation theoretic property that ${\rm…

In this paper, we give a concrete description of the two-fold cover of a simply connected, split real reductive group and its maximal compact subgroup as Chevalley groups. We define a representation of the maximal compact subgroup called…

Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…

We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…

Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…

We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators…

A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2,1) Lie algebra…

Let $G$ be a compact and connected Lie group and $PU(\mathcal H)$ be the group of projective unitary operators on a separable Hilbert space $\mathcal H$ endowed with the strong operator topology. We study the space $hom_{st}(G, PU(\mathcal…

We investigate the structure of the ring ${\mathbb D}_G(X)$ of $G$-invariant differential operators on a reductive spherical homogeneous space $X=G/H$ with an overgroup $\widetilde{G}$. We consider three natural subalgebras of ${\mathbb…

We study intertwining relations for matrix one-dimensional, in general, non-Hermitian Hamiltonians by matrix differential operators of arbitrary order. It is established that for any matrix intertwining operator Q_N^- of minimal order N…

An integral representation of the intertwining operator for the Dunkl operators associated with symmetric groups is derived for the class of functions of a single component. The expression provides a closed form formula for the reproducing…