Related papers: On weakly maximal representations of surface group…

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…

We develop the theory of maximal representations of the fundamental group of a compact connected oriented surface with boundary, into a group of Hermitian type. For any such representation we define the Toledo invariant, for which we…

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…

We consider irreducible lowest-weight representations of Cherednik algebras associated to certain classes of complex reflection groups in characteristic p. In particular, we study maximal graded submodules of Verma modules associated to…

We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

Let $\mathbb F$ be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in ${\rm Sp}(2n,\mathbb F)$. We show that ultralimits of maximal representations in…

We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irreducible representations of dimension at most n for a simple…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then apply our…

In this study, we introduce graded pseudo weakly prime submodules of G-graded R-modules, which are an extension of graded weakly prime ideals over G-graded rings. On the graded spectrum of graded pseudo weakly prime submodules, we…

Let $R$ be a ring and $n$, $k$ two non-negative integers. In this paper, we introduce the concepts of $n$-weak injective and $n$-weak flat modules and via the notion of special super finitely presented modules, we obtain some…

The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

We study the structure of minimal parabolic subgroups of the classical infinite dimensional real simple Lie groups, corresponding to the classical simple direct limit Lie algebras. This depends on the recently developed structure of…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

We prove that the mapping class group of a closed surface acts ergodically on connected components of the representation variety corresponding to a connected compact Lie group.

In this paper, we introduce a new algebraic type of `convexoid rings', and we give the definition of (weak) convexoid schemes, which share similar properties with ordinary schemes. As a result, we give a purely-algebraic construction of the…

In this article, we classify disconnected reductive groups over an algebraically closed field with a few caveats. Internal parts of our result are both a classification of finite groups and a classification of integral representations of a…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…