Related papers: Cuspidal integrals and subseries for $\mathrm{SL}(…

We study the microlocal properties of generalized Radon transforms over a family of quadric hypersurfaces whose centers lie on an orientable hypersurface $S$. The quadric surfaces we consider are level sets of the quadratic form associated…

We investigate the Radon transform for double fibrations of the horocycle spaces for the semisimple symmetric spaces with respect to the inclusion incidence relations. We present the inversion formula, support theorem and the range theorem…

In this paper we continue our program of extending the methods of geometric scattering theory to encompass the analysis of the Laplacian on symmetric spaces of rank greater than one and their geometric perturbations. Our goal here is to…

In our previous papers we repeatedly emphasized the special role in Quaternionic Analysis of the conformal group SU(2,2) and other real forms of its complexification SL(4,C). In particular, the natural product map of the left and right…

We consider the question: can the isotropy representation of an irreducible pseudo-Riemannian symmetric space be realized as a conformal holonomy group? Using recent results of Cap, Gover and Hammerl, we study the representations of…

The spectrum of a Gelfand pair $(K\ltimes N, K)$, where $N$ is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz $K$-invariant…

We extend the theorems of [G1] on $L^p$ to $L^p_s$ Sobolev improvement for translation invariant Radon and fractional singular Radon transforms over hypersurfaces, proving $L^p$ to $L^q_s$ boundedness results for such operators. Here $q…

We obtain the Plancherel decomposition for a reductive symmetric space in the sense of representation theory. Our starting point is the Plancherel formula for spherical Schwartz functions, obtained in part I (math.RT/0107063). The formula…

We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV…

It is common that a Sobolev space defined on $\mathbb{R}^m$ has a non-compact embedding into an $L^p$-space, but it has subspaces for which this embedding becomes compact. There are three well known cases of such subspaces, the Rellich…

In this work we construct new multidimensional families of complete minimal submanifolds, of the classical non-compact Riemannian symmetric spaces SL_n(R)/SO(n), Sp(n,R)/U(n), SO*(2n)/U(n) and SU*(2n)/Sp(n), of codimension two.

A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms.…

We study Gelfand pairs for locally compact quantum groups. We give an operator algebraic interpretation and show that the quantum Plancherel transformation restricts to a spherical Plancherel transformation. As an example, we turn the…

We consider two dimensional $\mathcal{N}=(4,4)$ superconformal field theories in the moduli space of symmetric orbifolds of K3. We complete a classification of the discrete groups of symmetries of these models, conditional to a series of…

We define and study the (minimal) Radon transform on a real symmetric variety.

We study proper isometric actions of non-compact semisimple Lie groups on pseudo-Riemannian symmetric spaces. Motivated by Okuda's classification of semisimple symmetric spaces admitting proper $SL(2,\mathbb{R})$-actions [J. Differential…

An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…

A number of years ago, Kumar Murty pointed out to me that the computation of the fundamental group of a Hilbert modular surface ([7],IV,${\S}$6), and the computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly…

In this paper we study the asymptotic distribution of the cuspidal spectrum of arithmetic quotients of the symmetric space S=SL(n,R)/SO(n). In particular, we obtain Weyl's law with an estimation on the remainder term. This extends results…

We study the symmetries of the soliton spectrum of a pair of T-dual integrable models, invariant under global $SL(2)_q\otimes U(1)$ transformations. They represent an integrable perturbation of the reduced Gepner parafermions, based on…