Related papers: Characters of SL(2) Representations of Groups

Let $\mathfrak{o}$ be the ring of integers of a non-archimedean local field with residue field of odd characteristic, $\mathfrak{p}$ be its maximal ideal and let $\mathfrak{o}_\ell = \mathfrak{o}/\mathfrak{p}^\ell$ for $\ell\ge 2$. In this…

We compute the Stiefel-Whitney Classes for representations of dihedral groups $D_m$ in terms of character values of order two elements. We also provide criteria to identify representations V which lift to the double covers of the orthogonal…

Let G be a subgroup of GL(V), where V is a finite dimensional vector space over a finite field of characteristic p >0. If det(g-1) = 0 for all g \in G then we call G a fixed-point subgroup of GL(V). Motivated in parallel by questions in…

We prove a division algorithm for group rings of high genus surface groups and use it to show that some $2$-complexes with surface fundamental groups are standard. We also give an application of division to cohomological dimension of…

This paper studies a subset of the free semi-group $F_k$ with letters in a field $k$ which has some interesting arithmetic and combinatorial properties.

We introduce the notion of stable representations, -- it is a new class of the representations of a certain class of groups which defined with positive definite functions which generalize the classical notion of the characters (or trace).…

We find normal forms for del Pezzo surfaces of degree $2$ over algebraically closed fields of characteristic $2$. For each normal form, we describe the structure of the group of automorphisms of the surface. In particular, we classify all…

Given a number field $K$, we show that certain $K$-integral representations of closed surface groups can be deformed to being Zariski dense while preserving many useful properties of the original representation. This generalizes a method…

In this paper, we study the geometric and dynamical properties of maximal representations of surface groups into Hermitian Lie groups of rank 2. Combining tools from Higgs bundle theory, the theory of Anosov representations, and…

We present a generalization of the sl(2) algebra where the algebraic relations are constructed with the help of a general function of one of the generators. When this function is linear this algebra is a deformed sl(2) algebra. In the…

We define semi-simple strata, semi-simple characters and semi-simple types in G_2(F). With some of these types we construct supercuspidal representations of this group.

We define the notion of a semicharacter of a group G : A function from the group to C*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is…

We build extensions of the arc rings, relate their centers to the cohomology rings of the Springer varieties, and categorify all level two representations of quantum sl(N).

Preface (A.Vershik) - about these texts (3.); I.Interpolation between inductive and projective limits of finite groups with applicatons to linear groups over finite fields; II.The characters of the groups of almost triangle matrices over…

The genus spectrum of a finite group $G$ is the set of all $g\geq 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating the…

We provide new group presentations for surface braid groups which are positive. We study some properties of such presentations and we solve the conjugacy problem in a particular case.

We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).

We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we…

We describe a construction of Schottky type subgroups of automorphism groups of partially cyclically ordered sets. We apply this construction to the Shilov boundary of a Hermitian symmetric space and show that in this setting Schottky…

We propose a family of new representations of the braid groups on surfaces that extend linear representations of the braid groups on a disc such as the Burau representation and the Lawrence-Krammer-Bigelow representation.