Related papers: Decomposition spaces in Combinatorics
A compact semisimple Lie algebra $\mathfrak{g}$ induces a Poisson structure $\pi$ on the unit sphere $S$ in $\mathfrak{g}^*$. We compute the moduli space of Poisson structures on $S$ around $\pi$. This is the first explicit computation of a…
In this article we study atomic and molecular decompositions in $2$-microlocal Besov and Triebel--Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the…
A complex hyperplane arrangement $\mathcal{A}$ is said to be decomposable if there are no elements in the degree 3 part of its holonomy Lie algebra besides those coming from the rank 2 flats. When this purely combinatorial condition is…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
The present paper is devoted to a theory of profile decomposition for bounded sequences in \emph{homogeneous} Sobolev spaces, and it enables us to analyze the lack of compactness of bounded sequences. For every bounded sequence in…
We obtain some simple relations between decomposition numbers of quantized Schur algebras at an n-th root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a…
Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…
This note explains how the two measures used to define the $\mu$-deformed Segal-Bargmann space are natural and essentially unique structures. As is well known, the density with respect to Lebesgue measure of each of these measures involves…
Contrary to the simple structure of the tensor product of the quaternionic Hilbert space, the octonionic situation becomes more involved. It turns out that an octonionic Hilbert space can be decomposed as an orthogonal direct sum of two…
Concentration compactness method is a powerful techniques for establishing existence of minimizers for inequalities and of critical points of functionals in general. The paper gives a functional-analytic formulation for the method in Banach…
The purpose of this short note is to illustrate the utility of (semi-) dendroidal objects in describing certain 'up-to-homotopy' operads. Specifically, we exhibit a semi-dendroidal space satisfying the Segal condition, whose evaluation at a…
This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
The configuration space of $n$ marked points on the complex plane is considered. We investigate a decomposition of this space by so-called Gauss-skizze i.e. a class of graphs being forests, introduced by Gauss. It is proved that this…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
Given an affine Poisson algebra, that is singular one may ask whether there is an associated symplectic form. In the smooth case the answer is obvious: for the symplectic form to exist the Poisson tensor has to be invertible. In the…
Interest in Conformal Field Theories and Quantum Field Theory lead physicists to consider configuration spaces of marked points on the complex projective line, $Conf_{0,d}(\mathbb{P})$. In this paper, a real semi-algebraic stratification of…
We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets,…
Compositionality is at the heart of computer science and several other areas of applied category theory such as computational linguistics, categorical quantum mechanics, interpretable AI, dynamical systems, compositional game theory, and…
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…