Related papers: Permutation-based presentations for Brin's higher-…

We show that the class of inductive limits of the representations of finite symmetric groups with simple spectrum coinsides with the class of Markov representations of the infinite symmetric group associated with Markov measures on the…

We construct a sequence of balanced finite presentations of the trivial group with two generators and two relators with the following property: The minimal number of relations required to demonstrate that a generator represents the trivial…

A new infinite class of Chern-Simons theories is presented using brane tilings. The new class reproduces all known cases so far and introduces many new models that are dual to M2 brane theories which probe a toric non-compact CY 4-fold. The…

We consider a group SO(2n+1) over a p-adic field, and tempered irreducible representations of this group, of unipotent reduction. We use the construction due to Lusztig of these representations. In an old paper with Moeglin, we have defined…

Matthew Brin and Patrick Dehornoy independently discovered a braided version BV of Thompson's group V. In this paper, we discuss some properties of BV that might make the group interesting for group based cryptography. In particular, we…

Given a finite-dimensional faithful representation $V$ of a linearly reductive group $G$ over a field $K=\bar K$, we consider the growth of the number of irreducible factors of $V^{\otimes n}$ when $n$ is large. We prove that there exist…

We study the bounded cohomology of certain groups acting on the Cantor set. More specifically, we consider the full group of homeomorphisms of the Cantor set as well as Thompson's group $V$. We prove that both of these groups are boundedly…

Talk given at the conference "Visions in Mathematics toward the year 2000", August 1999, Tel-Aviv.

We present a new method for showing that groups are virtually special. This is done by considering finite quotients and linear characters. We use this to show that an infinite family of groups, related to Bestvina-Brady groups and…

Given a semisimple stable autonomous tensor category over a field $K$, to any group presentation with finite number of generators we associate an element $Q(P)\in K$ invariant under the Andrews-Curtis moves. We show that in fact, this is…

This is the first of a three parts paper providing full details for our previous announcement in Pr\'epublications Orsay 2007-16, arXiv:0711.3579. Here we prove the results stated in the title.

The induced representation ${\rm Ind}_H^GS$ of a locally compact group $G$ is the unitary representation of the group $G$ associated with unitary representation $S:H\rightarrow U(V)$ of a subgroup $H$ of the group $G$. Our aim is to develop…

We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a…

Based on an idea in [Gan--Savin, Represent. Theory (2005)], we give a classification of minimal representations of connected simple real Lie groups not of type $A$. Actually, we prove that there exist no new minimal representations up to…

We provide an (almost) self-contained construction of the Witten-Reshetikhin-Turaev representations of the mapping class group. We describe its properties including its Hermitian structure, irreducibility and integrality (at prime level).…

The representation theory of the symmetric group has been intensively studied for over 100 years and is one of the gems of modern mathematics. The full transformation monoid $\mathfrak T_n$ (the monoid of all self-maps of an $n$-element…

The Maxwell group in 2+1 dimensions is given by a particular extension of a semi-direct product. This mathematical structure provides a sound framework to study different generalizations of the Maxwell symmetry in three space-time…

Infinite presentations are given for all of the higher Torelli groups of once-punctured surfaces. In the case of the classical Torelli group, a finite presentation of the corresponding groupoid is also given, and finite presentations of the…

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…

We introduce a new product for permutation groups. It takes as input two permutation groups, M and N, and produces an infinite group M [X] N which carries many of the permutational properties of M. Under mild conditions on M and N the group…