Related papers: Which reducible representations are Anosov?

We obtain restrictions on which groups can admit relatively Anosov representations into specified target Lie groups, by examining the topology of possible Bowditch boundaries and how they interact with the Anosov limit maps. For instance,…

Given a finite-dimensional faithful representation $V$ of a linearly reductive group $G$ over a field $K=\bar K$, we consider the growth of the number of irreducible factors of $V^{\otimes n}$ when $n$ is large. We prove that there exist…

In this survey, we shall be concerned with the category of finite-dimensional representations of the untwisted quantum affine algebras when the quantum parameter q is not a root of unity. We review the foundational results of the subject,…

For infinite reductive groups with Frobenius maps, we show that certain subquotients of abstract representations of the groups induced from 1-dimensional representations of Borel subgroups are irreducible.

A representation $\rho$ of a compact group $\mathbb{G}$ selects eigenvalues if there is a continuous circle-valued map on $\mathbb{G}$ assigning an eigenvalue of $\rho(g)$ to every $g\in \mathbb{G}$. For every compact connected…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

The aim of this work is to give a combinatorial way to describe all irreducible representations in case the super-dimension of $V$ is $(3|1)$.

Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…

We determine the irreducible representations of alternating and symmetric groups and their universal central extensions that contain a non-scalar element with all but one eigenvalues of multiplicity 1. The ground field is algebraically…

Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…

In this article, we classify disconnected reductive groups over an algebraically closed field with a few caveats. Internal parts of our result are both a classification of finite groups and a classification of integral representations of a…

We classify up to equivalence all finite-dimensional irreducible representations of PSL2(Z) whose restriction to the commutator subgroup is diagonalizable.

We show that if a cusped Borel Anosov representation from a lattice $\Gamma \subset \mathsf{PGL}_2(\mathbb{R})$ to $\mathsf{PGL}_d(\mathbb{R})$ contains a unipotent element with a single Jordan block in its image, then it is necessarily a…

In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.

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'…

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

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

Let $\Gamma$ be a one-ended, torsion-free hyperbolic group and let $G$ be a semisimple Lie group with finite center. Using the canonical JSJ splitting due to Sela, we define amalgam Anosov representations of $\Gamma$ into $G$ and prove that…

In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…