Related papers: Equivalence of diagonal contractions to generalize…

We prove that there exists just one pair of complex four-dimensional Lie algebras such that a well-defined contraction among them is not equivalent to a generalized IW-contraction (or to a one-parametric subgroup degeneration in…

We consider a class of generalized Inonu-Wigner contraction for semidirect product of two particularly related semisimple Lie (super)algebras. The special class of such contractions provides D=4 Maxwell algebra and recently introduced…

The development of the notion of group contraction first introduced by E. In{\"o}n{\"u} and E.P. Wigner in 1953 is briefly reviewed. The fundamental role of the idea of degenerate transformations is stressed. The significance of…

A generalised Weber function is given by $\w_N(z) = \eta(z/N)/\eta(z)$, where $\eta(z)$ is the Dedekind function and $N$ is any integer; the original function corresponds to $N=2$. We classify the cases where some power $\w_N^e$ evaluated…

Inversion theorems of Wiener type are essential tools in analysis and number theory. We derive a weighted version of an inversion theorem of Wiener type for general Dirichlet series from that of Edwards from 1957, and we outline an…

The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…

We introduce a duality for In\"{o}n\"{u}-Wigner contractions attached to real symmetric Lie algebras. Starting from a symmetric pair $(\mathfrak{g},\theta)$, we define a dual real form $\mathfrak{g}^{*}$ inside the complexification of…

Traces of large powers of real-valued Wigner matrices are known to have Gaussian fluctuations: for $A=\frac{1}{\sqrt{n}}(a_{ij})_{1 \leq i,j \leq n}\in \mathbb{R}^{n \times n}, A=A^T$ with $(a_{ij})_{1 \leq i \leq j \leq n}$ i.i.d.,…

It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…

We show that, under some mild hypotheses, the Gowers uniformity norms (both in the additive and in the hypergraph setting) are essentially equivalent to certain weaker norms which are easier to understand. We present two applications of…

Wigner's celebrated theorem, which is particularly important in the mathematical foundations of quantum mechanics, states that every bijective transformation on the set of all rank-one projections of a complex Hilbert space which preserves…

We perform a In\"on\"u--Wigner contraction on Gaudin models, showing how the integrability property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains,…

A generalization of Powers-St$\o$rmer's inequality for operator monotone functions on $[0, +\infty)$ and for positive linear functional on general $C^*$-algebras will be proved. It also will be shown that the generalized Powers-St$\o$rmer…

We establish a q-generalization of Gordon's theorem that the space of diagonal coinvariants has a quotient identified with a perfect representation of the rational double affine Hecke algebra. It leads to a simple proof of his theorem and…

We study the generalization of $m$-isometries and $m$-contractions (for positive integers $m$) to what we call $a$-isometries and $a$-contractions for positive real numbers $a$. We show that any Hilbert space operator, satisfying an…

We introduce a one parameter deformation of the Zwegers' $\mu$-function as the image of $q$-Borel and $q$-Laplace transformations of a fundamental solution for the $q$-Hermite-Weber equation. We further give some formulas for our…

In this work we present a number of generalizations of Wick's theorems on integrals with Gaussian weight to a larger class of weights which we call subgaussian. Examples of subgaussian contractions are that of Kac-Moody or Virasoro type,…

We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…

In this paper, we introduce a one parameter generalization of the famous B\"ottcher-Wenzel (BW) inequality in terms of a $q$-deformed commutator. For $n \times n$ matrices $A$ and $B$, we consider the inequality \[…

This paper forms part of a larger work where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of "global conformal invariants"; these are defined to be conformally invariant integrals of geometric scalars. The…