Related papers: Weyl group action on Radon hypergeometric function…

We study the Gaussian Radon transform in the classical Wiener space of Brownian motion. We determine explicit formulas for transforms of Brownian functionals specified by stochastic integrals. A Fock space decomposition is also established…

Non-Hermitian (NH) Hamiltonians describe open quantum systems, nonequilibrium dynamics, and dissipative processes. Although a rich range of single-particle NH physics has been uncovered, many-body phenomena in strongly correlated NH systems…

In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to superspace are studied. Previously, a Fourier transform in superspace was already studied, but with a different kernel. In this work, the…

We prove that if a countable discrete group $\Gamma$ is {\it w-rigid}, i.e. it contains an infinite normal subgroup $H$ with the relative property (T) (e.g. $\Gamma= SL(2,\Bbb Z) \ltimes \Bbb Z^2$, or $\Gamma = H \times H'$ with $H$ an…

A rational group of hermitian type is an algebraic group over the rational numbers whose symmetric space is a hermitian symmetric space. We assume such a group $G$ to be given, which we assume is isotropic. Then, for any rational parabolic…

The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that…

We consider the family of Hecke triangle groups $ \Gamma_{w} = \langle S, T_w\rangle $ generated by the M\"obius transformations $ S : z\mapsto -1/z $ and $ T_{w} : z \mapsto z+w $ with $ w > 2.$ In this case the corresponding hyperbolic…

We investigate the permutation modules associated to the set of $k$-dimensional faces of the hyperoctahedron in dimension $n$, denoted $H^{n}.$ For any $k\leq n$ such a module can be defined over an arbitrary field $F$, it is called a face…

The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In…

Let $\mathscr Q$ be the quaternion Heisenberg group, and let $\mathbf P$ be the affine automorphism group of $\mathscr Q$. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary…

We study covariance functions in the Gauss hypergeometric ($\mathcal{GH}$) class, a flexible family that encompasses the Generalized Wendland ($\mathcal{GW}$) and Mat\'ern ($\mathcal{MT}$) models. We derive sharp validity conditions,…

This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the Riemannain situation;…

Functional Hamilton-Jacobi (HJ) equation, the central equation of the holographic renormalization group (HRG), functional Schr\"{o}dinger equation, and generalized Wilson-Polchinski (WP) equation, the central equation of the functional…

Let $k$ be an infinite field of positive characteristic. We determine all homomorphisms between Weyl modules for $GLn(k)$, where one of the partitions is a hook. As a consequence we obtain a nonvanishing result concerning homomorphisms…

Denote by $Sp(k,l)$ the quaternionic symplectic group of signature $(k,l)$. We study the deformation rigidity of the embedding $Sp(k,l) \times Sp(1) \hookrightarrow H$, where $H$ is either $Sp(k+1,l)$ or $Sp(k,l+1)$, this is done by…

Motivated by collapsing of Riemannian manifolds and inhomogeneous scaling of left invariant Riemannian metrics on a real Lie group $G$ with a sub-group $H$, we introduce a family of interpolation equations on $G$ with a parameter…

We present a gauge invariant action for a superstring in the plane wave background with Ramond-Ramond (RR) five-form flux. The Wess-Zumino term is given explicitly in a bilinear form of the left invariant currents by introducing a fermionic…

We are given a finite group $H$, an automorphism $\tau$ of $H$ of order $r$, a Galois extension $L/K$ of fields of characteristic zero with cyclic Galois group $\langle\sigma\rangle$ of order $r$, and an absolutely irreducible…

We establish a fundamental connection between the geometric RSK correspondence and GL(N,R)-Whittaker functions, analogous to the well known relationship between the RSK correspondence and Schur functions. This gives rise to a natural family…

The self-dual double copy is further explored. In previous work, it has been shown that hyper-Hermitian manifolds also have associated the self-dual gauge theories via Kerr-Schild double copy. The self-dual double copy is generalized in the…