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A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…
The representations of a $k$-graph $C^*$-algebra $C^*(\Lambda)$ which arise from $\Lambda$-semibranching function systems are closely linked to the dynamics of the $k$-graph $\Lambda$. In this paper, we undertake a systematic analysis of…
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…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…
An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group…
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…
In this article, we introduce the singular twin monoid and its corresponding group, constructed from both algebraic and topological perspectives. We then classify all complex homogeneous $2$-local representations of this constructed group.…
We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt path algebras Chen's construction of irreducible representations of Leavitt path…
This paper aims to use topological methods to compute $\mathrm{Ext}$ between an irreducible representation of a finite monoid inflated from its group completion and one inflated from its group of units, or more generally coinduced from a…
We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.
Inspired by Ol'shanskii's work, we provide an axiomatic framework to describe certain irreducible unitary representations of non-discrete unimodular totally disconnected locally compact groups. We then look at the applications to certain…
We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…
With each resonance of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type, One can associate a residue representation. The purpose of this paper…
We show that if a group can be represented as a graph product of finite directly indecomposable groups, then this representation is unique.
Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…
We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.
A group is irreducibly represented if it has a faithful irreducible unitary representation. For countable groups, a criterion for irreducible representability is given, which generalises a result obtained for finite groups by W. Gasch\"utz…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
We review various notions of correspondences for locally compact groupoids with Haar systems, in particular a recent definition due to R.D. Holkar. We give the construction of the representations induced by such a correspondence. Finally,…
We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Cherednik algebras associated to the general and special…