Related papers: Low-dimensional indecomposable representations of …

We classify the possibilities for the fixed field of the kernel of an irreducible three-dimensional Artin representation of $\Q$ with solvable image ramified at one prime by using the classification of the finite irreducible subgroups of…

Let $G$ be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to $3$. We construct a canonical correspondence between irreducible characters of degree coprime to $3$ of $G$ and those…

We determine the group of reductive cohomological degree $3$ invariants of all split semisimple groups of types $B$, $C$, and $D$. We also present a complete description of the cohomological invariants. As an application, we show that the…

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…

Using a combinatorial description due to Jacon and Lecouvey of the wall crossing bijections for cyclotomic rational Cherednik algebras, we show that the irreducible representations $L_c(\lambda^\pm)$ of the rational Cherednik algebra…

We study the structure of the category of integrable level zero representations with finite dimensional weight spaces of affine Lie algebras. We show that this category possesses a weaker version of the finite length property, namely that…

We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…

We prove that there are no irreducible representations of $B_n$ of dimension $n+1$ for $n\geq 10.$

The purpose of this article is to describe the integral cohomology of the braid group B_3 and SL_2(Z) with local coefficients in a classical geometric representation given by symmetric powers of the natural symplectic representation. These…

The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…

For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our…

We construct a family of six dimensional block representations of the braid group $B_3$ on three strings. We show that some of these representations can be used to detect braid vertibility of some known knots and others of 9 and 10…

For any irreducible representation of a surface group into $\mathrm{SL}_2(\mathbb{C})$, we show that there exists a pants decomposition where the restriction to any pair of pants is irreducible and where no curve of the decomposition is…

We prove that the restriction of any absolutely irreducible representation of Steinberg's triality groups $^3D_4(q)$ in characteristic coprime to q to any proper subgroup is reducible

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

Let $A$ be a finite-dimensional algebra over an algebraically closed field. The problem of constructing indecomposable $A$-modules inductively from simple ones by means of exact sequences - called accessibility - is the starting point of…

It is known that the Lawrence-Krammer representation of the Artin group of type $A_{n-1}$ based on the two parameters $t$ and $q$ that was used by Krammer and independently by Bigelow to show the linearity of the braid group on $n$ strands…

We determine the derived representation types of algebras with radical square zero and give a description of the indecomposable objects in their bounded derived categories.