Related papers: Knapp-Stein type intertwining operators for symmet…

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target…

Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted…

Let $ G $ be a connected reductive algebraic group over $ \C $. We denote by $ K = (G^{\theta})_{0} $ the identity component of the fixed points of an involutive automorphism $ \theta $ of $ G $. The pair $ (G, K) $ is called a symmetric…

We construct and normalise intertwining operators at the level of Hilbert modules describing the principal series of SL(2). Normalisation is achieved through the use of a Fourier transform defined on some homogenous space and twisted by a…

We study the principal subspaces, introduced by B. Feigin and A. Stoyanovsky, of the level 1 standard modules for $\hat{\goth{sl}(l+1)}$ with $l \geq 2$. In this paper we construct exact sequences which give us a complete set of recursions…

Let $G$ be a direct product of inner forms of general linear groups over non-archimedean locally compact fields of residue characteristic $p$ and let $K^1$ be the pro-$p$-radical of a maximal compact open subgroup of $G$. In this paper we…

We introduce intertwining operators among twisted modules or twisted intertwining operators associated to not-necessarily-commuting automorphisms of a vertex operator algebra. Let $V$ be a vertex operator algebra and let $g_{1}$, $g_{2}$…

In the present paper the algebras of functions on quantum homogeneous spaces are studied. The author introduces the algebras of kernels of intertwining integral operators and constructs quantum analogues of the Poisson and Radon transforms…

In exactly solvable quantum-mechanical systems, ladder and intertwining operators play a central role because, if they are found, the energy spectra can be obtained algebraically. In this paper, we propose the spectral intertwining relation…

We give explicit formulas for the intertwinors on the differential form bundles over $S^{p-1} \times S^{q-1}$ with the standard pseudo-Riemannian metric $g=-g_{{}_{S^{p-1}}}+g_{{}_{S^{q-1}}}$ of signature $(p-1,q-1)$. As a special case, we…

This paper presents explicit formulas for intertwining operators of the quantum group $U_q(sl_2)$ acting on tensor products of Verma modules. We express a first set of intertwining operators (the holographic operators) in terms of the…

We prove existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to…

In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the notion of intertwining operator algebra, a nonmeromorphic generalization of the notion of vertex operator algebra involving monodromies. The problem of constructing…

In this paper, we introduce a generalization of G-opers for arbitrary parabolic subgroups P<G. For parabolic subgroups associated to even nilpotents, we parameterize (G,P)-opers by an object generalizing the base of the Hitchin fibration.…

In this note, we express explicitly the Dunkl kernel and generalized Bessel functions of type $A_{n-1}$ by the Humbert's function $\Phi_{2}^{(n)}$, with one variable specified. The obtained formulas lead to a new proof of Xu's integral…

Let F be a p-adic field of odd residual characteristic. Let G(n) and G`(n) be the metaplectic double covers of the general symplectic group and the symplectic group attached to the 2n dimensional symplectic space over F. Let T be a genuine,…

General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in…

We study operator mixing, due to planar one-loop corrections, for composite operators in D=4 supersymmetric theories. We present some N=1,2 Yang-Mills and Wess-Zumino models, in which the planar one-loop anomalous dimension matrix in the…

We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…

We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the following reductive groups over number fields:…