Related papers: Nonlinearity of matrix groups

Let $p>3$ be a prime number. We compute the rings of invariants of the elementary abelian $p$-group $(\mathbb Z/p\mathbb Z)^r$ for $3$-dimensional generic representations. Furthermore we show that these rings of invariants are complete…

We give some examples of non-complete invariant affine connections on nilpotent and filiform Lie groups. This permits to describe non-nilpotent faithful representations on the model of filiform n-dimensional Lie algebras and, in particular,…

Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated

The work proves that, for three-dimensional upper triangular groups over a field of odd characteristic with an abelian unipotent subgroup, the ring of invariants is polynomial if and only if the unipotent subgroup is generated by…

Falbel, Koseleff and Rouillier computed a large number of boundary unipotent CR representations of fundamental groups of non compact three-manifolds. Those representations are not always discrete. By experimentally computing their limit…

Let $\Gamma$ be a finitely generated group of matrices over $\mathbb{C}$. We construct an isometric action of $\Gamma$ on a complete CAT(0) space $X$ such that the restriction of this action to any subgroup of $\Gamma$ containing no…

We show that every complete noetherian local commutative ring R with residue field k can be realized as a universal deformation ring of a continuous linear representation of a profinite group. More specifically, R is the universal…

As the 3-string braid group B(3) and the modular group PSL(2,Z) are both of wild representation type one cannot expect a full classification of all their finite dimensional simple representations. Still, one can aim to describe 'most'…

Let $G$ be a complex, linear algebraic group acting on an algebraic space $X$. The purpose of this paper is to prove a Riemann-Roch theorem (Theorem 5.3) which gives a description of the completion of the equivariant Grothendieck group…

In this paper, we answer affirmatively a question of H S Sim on representations in characteristic $0$, for a class of metabelian groups. Moreover, we provide examples to point out that the analogous answer is no longer valid if the solvable…

Let $F$ be an infinite division ring, $V$ be a left $F$-vector space, $r>0$ be an integer. We study the structure of the representation of the linear group $\mathrm{GL}_F(V)$ in the vector space of formal finite linear combinations of…

We study a coarse moduli space of irreducible representations of the group of unipotent matrices of order $\mathbb{4}$ over the ring of integers which have finite weight. All such representations are known to be monomial. To describe a…

We prove using a novel random matrix model that all right-angled Artin groups have a sequence of finite dimensional unitary representations that strongly converge to the regular representation. We deduce that this result applies also to:…

Let $\ell$ be a prime and let $q$ be a prime power not divisible by $\ell$. Put $G=\mathrm{GL}_n(\mathrm{F}_q)$ and fix an irreducible cuspidal representation, $\bar{\pi}$, of $G$ over a sufficiently large finite field, $k$, of…

We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include…

We show that if $X$ is an indecomposable $PD_3$-complex and $\pi_1(X) is the fundamental group of a reduced finite graph of finite groups but is not virtually cyclic then $X$ is orientable, the underlying graph is a tree, all the edge…

An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. The group ring $RG$ of a finite group $G$ is isomorphic to the set of {\em group ring matrices} over $R$. It is shown that…

In a previous paper I have defined a new basis for the representation ring of a Weyl group. In this paper we show that the new basis is related to the standard basis by an upper triangular unipotent matrix. We also give a new…

For certain rings $\mathcal{R}$, we construct explicit matrices representing nonzero classes in the algebraic $K$ theory group $NK_{1}(\mathcal{R})$.

Let $X$ be a variety (possibly non-complete or singular) over a finitely generated field $k$ of characteristic $0$. For a prime number $\ell$, let $\rho_\ell$ be the Galois representation on the first $\ell$-adic cohomology of $X$. We show…