Related papers: Endotrivial modules for infinite groups

We relate endotrivial representations of a finite group in characteristic p to equivariant line bundles on the simplicial complex of non-trivial p-subgroups, by means of weak homomorphisms.

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.

We determine the finite groups whose real irreducible representations have different degrees.

We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.

These notes give a short introduction to finite Coxeter groups, their classification, and some parts of their representation theory, with a focus on the infinite families. They are based on lectures delivered by the author at the…

We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and…

Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures,…

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…

In this note we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if $H$ is a finitely generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic, then $H$ has…

The works prsented in this habilitation thesis can be gathered in six themes. Works on the implicit function theorem and the geometry of numerical schemes. On the existence of an exponential map on an infinite dimensioal Lie group. Holonomy…

These notes are based on a talk given at the Summer School "Infinite-dimensional representations of finite-dimensional algebras" held at the University of Manchester in September 2015. They intend to provide a brief introduction to the…

In this note several computations of equivariant cohomology groups are performed. For the compactly supported equivariant cohomology, the notion of infinitesimal index developed in arXiv:1003.3525, allows to describe these groups in terms…

Big mapping class groups are the mapping class groups of infinite-type surfaces, that is, surfaces whose fundamental groups are not finitely generated. While mapping class groups of finite-type surfaces have been extensively studied, the…

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

These are the lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute. I give an introduction to Higgs bundles and their application to the study of character varieties for surface group…

Lectures at the CRM-CAP Summer School 'Particles and Fields 94' August 16-24 1994, Banff, Alberta, Canada.

We discuss the structure of finite groups for which the projective indecomposable modules have special given dimensions. In particular, we prove the converse of Fong's dimension formula for $p$-solvable groups. Furthermore, we characterize…

We define new topological invariants for Anosov representations and study them in detail for maximal representations of the fundamental group of a closed oriented surface into the symplectic group.