Related papers: Which reducible representations are Anosov?

For uniform lattices $\Gamma$ in rank 1 Lie groups, we construct Anosov representations of virtual doubles of $\Gamma$ along certain quasiconvex subgroups. We also show that virtual HNN extensions of these lattices over some cyclic…

Let G be a connected reductive group defined over a finite field F_q. We give a parametrization of the irreducible representations of G(F_q) in terms of (twisted) categorical centres of various monoidal categories associated to G. (Results…

In this paper, we construct cataclysm deformations for $\theta$-Anosov representations into a semisimple non-compact connected real Lie group $G$ with finite center, where $\theta \subset \Delta$ is a subset of the simple roots that is…

Anosov representations were introduced by F. Labourie [18] for fundamental groups of closed negatively curved surfaces, and generalized by O. Guichard and A. Wienhard [19] to representations of arbitrary Gromov hyperbolic groups into real…

We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…

In this paper we provide a general condition for the reducibility of the Reshetikhin-Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a…

We consider the irreducible representations each of dimension 2 of the necklace braid group $\mathcal{NB}_n$ ($n=2,3,4$). We then consider the tensor product of the representations of $\mathcal{NB}_n$ ($n=2,3,4$) and determine necessary and…

Crystabelline representations are representations of the absolute Galois group $G_{\mathbb{Q}_p}$ over $\mathbb{Q}_p$ that become crystalline on $G_{F}$ for some abelian extension $F/\mathbb{Q}_p$. Their relation to modular forms is that…

We determine semisimple reductions of irreducible, 2-dimensional crystalline representations of the absolute Galois group $\text{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_{p^f})$. To this end, we provide explicit representatives for the…

This paper is the first part of a series of papers aimed at improving the classification by Formanek of the irreducible representations of Artin braid groups of small dimension. In this paper we classify all the irreducible complex…

We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…

This paper describes irreducible representations in category O of the rational Cherednik algebra H_c(H_3,h) associated to the exceptional Coxeter group H_3 and any complex parameter c. We compute the characters of all these representations…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…

We announce here a number of results concerning representation theory of the algebra $R=k<x,y>/ (xy-yx-y^2)$, known as Jordan plane (or Jordan algebra). We consider the question on 'classification' of finite-dimensional modules over the…

Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…

We study the representation theory of quantizations of Gieseker moduli spaces. We describe the categories of finite dimensional representations for all parameters and categories O for special values of parameters. We find the values of…

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

Anosov families are non-stationary dynamical systems with hyperbolic behavior. Non-trivial examples of Anosov families will be given in this paper. We show the existence of invariant manifolds, the structrural stability and a…

We establish exponential decay of correlations of all orders for locally $G$-accessible isometric extensions of transitive Anosov flows, under the assumption that the strong stable and strong unstable foliations of the base Anosov flow are…