Related papers: Irreducible adjoint representations in prime power…

The SU(2) TQFT representation of the mapping class group of a closed surface of genus g, at a root of unity of prime order, is shown to be irreducible. Some examples of reducible representations are also given.

In this letter we show that for certain infinite families of modular forms of growing level it is possible to have a control result for the exceptional primes of the attached Galois representations. As an application, a uniform version of a…

We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of $GL_{n}(q)$ on restriction to $SL_{n}(q)$. Combined with a recent result of C. Bonnafe, this yields a canonical labeling for…

We show that for any finite-dimensional algebra $\Lambda$ of infinite representation type, over a perfect field, there is a bounded principal ideal domain $\Gamma$ and a representation embedding from $\Gamma -$mod into $\Lambda -$mod. As an…

Given a pair of n-dimensional complex Galois representations over Q, we define their matching density to be the density, if it exists, of the set of places at which the traces of Frobenius of the two Galois representations are equal. We…

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

In the paper we study irreducible representations of some nilpotent groups of finite abelian total rank. The main result of the paper states that if a torsion-free minimax group $G$ of nilpotency class 2 admits a faithful irreducible…

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…

We construct a new family of irreducible unitary representations of a finitely generated virtually free group L. We prove furthermore a general result concerning representations of Gromov hyperbolic groups that are weakly contained in the…

Let $L/K$ be a Galois extension of number fields and let $G=\mathrm{Gal}(L/K)$. We show that under certain hypotheses on $G$, for a fixed prime number $p$, Leopoldt's conjecture at $p$ for certain proper intermediate fields of $L/K$ implies…

For an additive polynomial and a positive integer, we define an irreducible smooth representation of a Weil group of a non-archimedean local field. We study several invariants of this representation. We deduce a necessary and sufficient…

In this paper we study some algebraic properties of the rack structure as well as the representation theory of it, following the ideas given by M. Elhamdadi and E. M. Moutuou in \cite{Elhamdadi}. We establish a correspondence between the…

We consider the problem of determining the relationship between two representations knowing that some tensor or symmetric power of the original represetations coincide. Combined with refinements of strong multiplicity one, we show that if…

Each irreducible representation of the motion group of the plane has a unique maximal inductive algebra, and it is self adjoint.

We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…

Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these…

We undertake a systematic study of irreducible affine isometric actions of locally compact groups on Hilbert spaces. It turns out that, while that are a few parallels of this study to the by now classical theory of irreducible unitary…

We construct and study in detail various dual pairs acting on some Fock representations between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit…

In this paper, we prove new instances of the inverse Galois problem over global function fields for finite groups of Lie type. This is done by constructing compatible systems of $\ell$-adic Galois representations valued in a semisimple…

We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.