Related papers: Modular Representations of Profinite Groups

Just infinite groups play a significant role in profinite group theory. For each $c \geq 0$, we consider more generally JNN$_c$F profinite (or, in places, discrete) groups that are Fitting-free; these are the groups $G$ such that every…

For modules over group rings we introduce the following numerical parameter. We say that a module A over a ring R has finite r-generator property if each f.g. (finitely generated) R-submodule of A can be generated exactly by r elements and…

Let G be a reductive complex algebraic group and V a finite-dimensional G-module. From elements of the invariant algebra C[V]^G we obtain by polarization elements of C[kV]^G, where k\geq 1 and kV denotes the direct sum of k copies of V. For…

The Lannes-Quillen theorem relates the mod-$p$ cohomology of a finite group $G$ with the mod-$p$ cohomology of centralizers of abelian elementary $p$-subgroups of $G$, for $p>0$ a prime number. This theorem was extended to profinite groups…

The 'degree of k-step nilpotence' of a finite group G is the proportion of the tuples (x_1,...,x_{k+1}) in G^{k+1} for which the simple commutator [x_1,...,x_{k+1}] is equal to the identity. In this paper we study versions of this for an…

Let V be a finite faithful completely reducible FG-module for a finite field F and a finite group G. In various cases explicit linear bounds in |V| are given for the numbers of conjugacy classes k(GV) and k(G) of the semidirect product GV…

We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group $G$ of finite rank over a field $k$. It was shown that the existence of such representations strongly depends on…

We investigate purities determined by classes of finitely presented modules including the correspondence between purities for left and right modules. We show some cases where purities determined by matrices of given sizes are different.…

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…

Let $\mathfrak C$ be a class of finite groups which is closed for subgroups, quotients and direct products. Given a profinite group $G$ and an element $x\in G$, we denote by $P_{\mathfrak{C}}(x,G)$ the probability that $x$ and a randomly…

We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…

We investigate infinite dimensional modules for a linear algebraic group $\mathbb G$ over a field of positive characteristic $p$. For any subcoalgebra $C \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we consider…

We survey the development and status quo of a subject best described as "generic representation theory of finite dimensional algebras", which started taking shape in the early 1980s. Let $\Lambda$ be a finite dimensional algebra over an…

We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra $kG$ of a finite group $G$ of Lie type defined over a finite field of odd characteristic $p$, where $k$ is an arbitrary field of…

In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras. We mainly focus on the finite-dimensional representations…

We give a general theory of generalised inverses and we explain the link with the theory of finitely generated projective modules. All the paper is written in constrctive mathematics in Bishop style. So all results do have a clear…

We introduce the notion of a neutral representation of a finite group, or finite group scheme, $G$; a representation $V$ with the property that if a gerbe $\mathcal{G}$ over a field $k$ that is a form of the classifying stack $\mathcal{B}…

By work of De Concini, Kac and Procesi the irreducible representations of the non-restricted specialization of the quantized enveloping algebra of the Lie algebra g at the roots of unity are parametrized by the conjugacy classes of a group…

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal…