Related papers: W_{N+1}-constraints for singularities of type A_N
We study the behavior of the spectrum of the Dirac operator together with a symmetric $W^{1, \infty}$-potential on spin manifolds under a collapse of codimension one with bounded sectional curvature and diameter. If there is an induced spin…
We examine the first-order Einstein-Cartan (EC) action in 2+1 dimensions, including a cosmological term and its supersymmetric extension. In this setting the spin connection can be expressed as an axial vector, yielding an action that is…
A Schroedinger type equation on the superspace R^{D|2n} is studied, which involves a potential inversely proportional to the negative of the osp(D|2n) invariant "distance" away from the origin. An osp(2,D+1|2n) dynamical supersymmetry for…
Let $G/H$ be a $p$-adic symmetric space. We compute explicitly the higher relative extension groups for all discrete series representations of $G$ in two examples: the symplectic case and the linear case. The results have immediate…
We study the properties of Wilson loops in three dimensional non-compact U(1) gauge theories with global abelian symmetries. We use duality in the continuum and on the lattice, to argue that close to the critical point between the Higgs and…
We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity function are…
We discuss the representation theory of $H_f$, which is a deformation of the symplectic oscillator algebra $sp(2n) \ltimes h_n$, where $h_n$ is the ((2n+1)-dimensional) Heisenberg algebra. We first look at a more general setup, involving an…
We extend the theory of topological recursion by considering Airy structures whose partition functions are highest weight vectors of particular $\mathcal{W}$-algebra representations. Such highest weight vectors arise as partition functions…
The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with…
The generalized curvature tensor and Christoffel symbols are determined in AdS_{d+1} background by a modified ansatz of the de Wit - Freedman type by imposing gauge invariance. The resulting set of recurrence relations and difference…
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$. Noteworthy, we admit negative values of the…
In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators $L$ with singular…
Let $A_\infty ^+$ denote the class of one-sided Muckenhoupt weights, namely all the weights $w$ for which $\mathsf M^+:L^p(w)\to L^{p,\infty}(w)$ for some $p>1$, where $\mathsf M^+$ is the forward Hardy-Littlewood maximal operator. We show…
Let $G={\rm GL}_n$ be the general linear group over an algebraically closed field $k$, let $\mathfrak g=\mathfrak gl_n$ be its Lie algebra and let $U$ be the subgroup of $G$ which consists of the upper uni-triangular matrices. Let…
We provide novel linear combination of unitaries decompositions for a class of discrete elliptic differential operators. Specifically, Poisson problems augmented with periodic, Dirichlet, Neumann, Robin, and mixed boundary conditions are…
For a reductive group $G$, we introduce a notion of singular support for cocomplete dualizable DG-categories equipped with a strong $G$-action. This is done by considering the singular support of the sheaves of matrix coefficients arising…
We extend the classical regularity theorem of elliptic operators to maximally hypoelliptic differential operators. More precisely, given vector fields $X_1,\ldots,X_m$ on a smooth manifold which satisfy H\"ormander's bracket generating…
We prove versions of super spin-charge separation for all three of the symmetry groups SU(N), Sp(2N), and SO(N) of disordered Dirac fermions in 2+1 dimensions, which involve the supercurrent-algebras gl (1|1)_{N}, osp(2|2)_{-2N}, and…
In this letter we study the dilatonic corrections to the static gauge potential between heavy sources. These corrections come from the solutions to the the lowest order beta equations. In the energetically favoured branch, the potential…
Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for…