Related papers: The Leray transform: factorization, dual $CR$ stru…
For the p-adic group G=SL (2) , we present results of the computations of the sums of the Bernstein projectors of a given depth. Motivation for the computations is based on a conversation with Roger Howe in August 2013. The computations are…
We detail an explicit construction of ordinary irreducible representations for the family of finite groups $SL_2({\mathbb Z} /p^n {\mathbb Z})$ for odd primes $p$ and $n\geq 2$. For $n=2$, the construction is a complete set of irreducible…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
The systematic study of CR manifolds originated in two pioneering 1932 papers of \'Elie Cartan. In the first, Cartan classifies all homogeneous CR 3-manifolds, the most well-known case of which is a one-parameter family of left-invariant CR…
Special fibrations of toric varieties have been used by physicists, e.g. the school of Candelas, to construct dual pairs in the study of Het/F-theory duality. Motivated by this, we investigate in this paper the details of toric morphisms…
We classify locally defined non-spherical real-analytic hypersurfaces in complex space whose Levi form has no more than one negative eigenvalue and for which the dimension of the group of local CR-automorphisms has the second largest value.
This paper explores Paley-Wiener type theorems within the framework of hypercomplex variables. The investigation focuses on a space-fractional version of the Dirac operator $\mathbf{D}_\theta^{\alpha}$ of order $\alpha$ and skewness…
We present a unified framework demonstrating how the spinor complex Lorentz group SL(2,C)/Z\_2 is realized as a canonical subgroup within a four-dimensional complex Riemannian manifold. Building on the complex, holomorphic metric extension…
We consider the three-dimensional Heisenberg group, equipped with any left-invariant metric, either Lorentzian or Riemannian. We completely classify their affine vector fields and investigate their relationship with Killing vector fields…
We develop a formalism with two different UV cutoff scales, one for space and one for time, appropriate for the richer structure of non-Lorentz invariant quantum field theories. In this formalism there are two different beta-functions for…
A translation surface in the Heisenberg group is constructed as the product of two planar curves. We classify a type of such surfaces with vanishing intrinsic curvature by analyzing the determinant of their Gauss map
The notion of Fourier transformation is described from an algebraic perspective that lends itself to applications in Symbolic Computation. We build the algebraic structures on the basis of a given Heisenberg group (in the general sense of…
We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and…
We first construct a space $\mathcal{W}\left( \mathbb{R}_{\text{c}} ^{n}\right) $ whose elements are test functions defined in $\mathbb{R} _{\text{c}}^{n}=\mathbb{R}^{n}\cup\left\{ \mathbf{\infty}\right\} ,$ the one point compactification…
We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one…
We work in a first-order setting where structures are spread out over a metric space, with quantification allowed only over bounded subsets. Assuming a doubling property for the metric space, we define a canonical {\em core} $\mathcal{J}$…
We construct normal forms for Levi degenerate hypersurfaces of finite type in $\mathbb C^2$. As one consequence, an explicit solution to the problem of local biholomorphic equivalence is obtained. Another consequence determines the…
In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta \geq 0$ is a parameter. As $d$ and $\alpha$ vary, the model…
Let $\E$ be a finite dimensional Hilbert space. This note finds all factorizations of the right shift semigroup $\S^\E=(S_t^\E)_{t\ge 0}$ on $L^2(\R_+,\E)$ into the product of $n$ commuting contractive semigroups, i.e., characterizes all…
We solve a problem posed by Cardinali and Sastry [2] about factorization of $2$-covers of finite classical generalized quadrangles. To that end, we develop a general theory of cover factorization for generalized quadrangles, and in…