相关论文: Euler-Poincar\'{e} formulae for positive depth Ber…

Starting from basic identities of the group E8, we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E7xSU(2) and then of E6xU(1). This procedure provides a systematic approach to…

A non-standard quantum deformation of the Poincar\'e algebra is presented in a null-plane framework for 1+1, 2+1 and 3+1 dimensions. Their corresponding universal $R$-matrices are obtained in a factorized form by choosing suitable bases…

The non-standard (Jordanian) quantum deformations of $so(2,2)$ and (2+1) Poincar\'e algebras are constructed by starting from a quantum $sl(2,\R)$ basis such that simple factorized expressions for their corresponding universal $R$-matrices…

We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincar\'{e} profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by…

It is well known that the Fourier--Bohr coefficients of regular model sets exist and are uniformly converging, volume-averaged exponential sums. Several proofs for this statement are known, all of which use fairly abstract machinery. For…

In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…

On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincar\'{e} group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the…

The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible…

We continue the $U$-bound program initiated in [J. Funct. Anal. 258, 814-851 (2010)] and prove super-Poincar\'e inequalities for a class of subelliptic probability measures defined on M\'etivier groups, the main ingredient in the proof…

Let G be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit O through a…

We prove an Induction Equivalence and a Kashiwara Equivalence for coadmissible equivariant D-modules on rigid analytic spaces. This allows us to completely classify such objects with support in a single orbit of a classical point with…

In this short note, we provide a quantitative global Poincar\'e inequality for one forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on Ricci…

In this paper, we treat $\mathscr{D}$-modules on the basic affine space $G/U$ and their global sections for a semisimple complex algebraic group $G$. Our aim is to prepare basic results about large non-irreducible modules for the branching…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

The primary purpose of this paper concerns the relation of (compact) generalized manifolds to finite Poincar\'{e} duality complexes (PD complexes). The problem is that an arbitrary generalized manifold $X$ is always an ENR space, but it is…

We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As…

In this paper we consider a novel statistical inverse problem on the Poincar\'{e}, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of $2\times2$ real…

We study a Riemannian manifold equipped with a density which satisfies the Bakry--\'Emery Curvature-Dimension condition (combining a lower bound on its generalized Ricci curvature and an upper bound on its generalized dimension). We first…

Four-dimensional extended: Poincar\'e, AdS-Lorentz and Maxwell algebras, are obtained by expanding an extension of de Sitter or conformal algebra, SO(4,1) or SO(3,2). The procedure can be generalized to obtain a new family of extended…

An explicit understanding of the (category of all smooth, complex) representations of p-adic groups provides an important tool not just within representation theory. It also has applications to number theory and other areas, and, in…