Related papers: Measures for the colored circle
Relative dimensions of isotypic components of N-th order tensor representations of the symmetric group on n letters give a Plancherel-type measure on the space of Young diagrams with n cells and at most N rows. It was conjectured by G.…
Given a measure equivalence coupling between two finitely generated groups, Delabie, Koivisto, Le Ma\^itre and Tessera have found explicit upper bounds on how integrable the associated cocycles can be. We extend these results to the broader…
We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction…
[PLEASE SEE COMMENT] We consider the isomorphism problem for finite abelian groups and finite meta-cyclic groups. We prove that for a dense set of positive integers $n$, isomorphism testing for abelian groups of black-box type of order $n$…
We consider a gas whose each particle is characterised by a pair $(x,v_x)$ with the position $x\in \mathbb R^d$ and the velocity $v_x\in \mathbb R^d_0= \mathbb R^d\setminus \{0\}$. We define Gibbs measures on the cone of vector-valued…
We study various optimality criteria for quantum observables. Observables are represented as covariant positive operator valued measures and we consider the case when the symmetry group is compact. Phase observables are examined as an…
Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially $q$-analogues, have useful interpretations related to actions and representations of the cyclic group. We propose a definition of sieving for an…
In any category with a reasonable notion of cover, each object has a group of scissors automorphisms. We prove that under mild conditions, the homology of this group is independent of the object, and can be expressed in terms of the…
We establish an area-type formula for the intrinsic spherical Hausdorff measure of every regular curve embedded in an arbitrary graded group.
The aim of this note is to explain a generalization to the real case of a well known result on the automorphism group of an unbounded tube type symmetric domain in a complex vector space of finite dimension.
We study concentration of measure in Lie group actions. We define the notion of concentration locus of a flag sequence of Lie groups. Some examples of infinite group action on an infinite dimensional compact and non compact manifold show…
Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank-$D$…
We study domains in complex $n$-space with automorphism group that does not depend on the full $n$ dimensions of the ambient space. A sufficient geometric condition is obtained to guarantee that a domain has such a "thin" automorphism…
Let $I(X,R)$ be the incidence algebra of the preordered set $X$ over the ring $R$. In the case of a finite connected partially ordered set $X$, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group…
The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.
In this paper we study applications of U-bounds to coercive and isoperimetric problems for probability measures on finite and infinite products of H-type groups.
Which combinatorial sequences correspond to moments of probability measures on the real line? We present a generating function, in the form of a continued fraction, for a fourteen-parameter family of such sequences and interpret these in…
We formulate Lehmer's Problem about the Mahler measure of polynomials for general compact abelian groups, introducing a Lehmer constant for each such group. We show that all nontrivial connected compact groups have the same Lehmer constant,…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
We present an analytical approach to evaluate the geometric measure of multiparticle entanglement for mixed quantum states. Our method allows the computation of this measure for a family of multiparticle states with a certain symmetry and…