Related papers: Representation stability of power sets and square …
In this paper, we define a set which has a finite group action and is generated by a finite color set, a set which has a finite group action, and a subset of the set of non negative integers. we state its properties to apply one of solution…
The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
Homological stability has shown itself to be a powerful tool for the computation of homology of families of groups such as general linear groups, mapping class groups or automorphisms of free groups. We survey here tools and techniques for…
We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
For any set representation (permutation representation) of the symmetric group $S_n$, we give combinatorial interpretation for coefficients of its Frobenius character expanded in the basis of monomial symmetric functions.
This paper is dedicated to the study of the stability of multiplicities of group representations.
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
The representation of the conformal group (PSU(2,2)) on the space of solutions to Maxwell's equations on the conformal compactification of Minkowski space is shown to break up into four irreducible unitarizable smooth Fr\'echet…
Some of the most classically relevant Hyperplane arrangements are the Braid Arrangements $B_n$ and their associated compliment spaces $\mathcal{F}_n$. In their recent work, Tsilevich, Vershik, and Yuzvinsky construct what they refer to as…
The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from…
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group $S_n$ on the cohomology of the configuration space of $n$ ordered points in $\mathbf{R}^d$. This cohomology is known to…
Here we consider two algebras, a free unital associative complex algebra (denoted by ${\mathcal{B}}$) equiped with a multiparametric \textbf{\emph{q}}-differential structure and a twisted group algebra (denoted by ${\mathcal{A}(S_{n})}$),…
We investigate the density of square-free values of polynomials with large coefficients over the rational function field $\mathbb{F}_q[t]$. Some interesting questions answered as special cases of our results include the density of…
Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.
This paper investigates the critical group of a faithful representation of a finite group. It computes the order of the critical group in terms of the character values, and gives some restrictions on its subgroup structure. It also computes…