Related papers: Generalised Gabriel-Roiter measure and thin repres…

Let G be a Lie group and Q a quiver with relations. In this paper, we define G-valued representations of Q which directly generalize G-valued representations of finitely generated groups. Although as G-spaces, the G-valued quiver…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum mechanical Poincar\'e group $\pt$. `Extended' refers to the extension of the 10 parameter Lie group that is the…

EI-categories are a simultaneous generalisation of finite groups and finite quivers without oriented cycles. It is therefore a natural question to ask for a characterisation of finite representation type. For special classes of…

We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…

Firstly, bilinear Fourier Restriction estimates --which are well-known for free waves-- are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications…

Let $Q$ be an $n$-Kronecker quiver, i.e., a quiver with two vertices, labeled by 1 and 2, and $n$ arrows from 2 to 1. We show that there are infinitely many Gabriel-Roiter measures admitting no direct predecessors.

A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…

We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…

We prove one direction of a recently posed conjecture by Gan-Gross-Prasad, which predicts the branching laws that govern restriction from p-adic $GL_n$ to $GL_{n-1}$ of irreducible smooth representations within the Arthur-type class. We…

Two representations of a reductive group G are spectrally equivalent if the same irreducible representations appear in both of them. The semigroup of finite dimensional representations of G with tensor product and up to spectral equivalence…

We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study…

We study representations of a Leavitt path algebra $L$ of a finitely separated digraph $\Gamma$ over a field. We show that the category of $L$-modules is equivalent to a full subcategory of quiver representations. When $\Gamma$ is a…

Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation…

A theorem of Glimm states that representation theory of an NGCR C*-algebra is always intractable, and the Cuntz algebra O_N is a case in point. The equivalence classes of irreducible representations under unitary equivalence cannot be…

An efficient and compact approach to the inclusion of dissipative effects in Non-Equilibrium Green's Function (NEGF) simulations of electronic systems is introduced. The algorithm is based on two well known methods in the literature,…

The notion of a glider representation of a chain of normal subgroups of a group is defined by a new structure, i.e. a fragment for a suitable filtration on the group ring. This is a special case of general glider representations defined for…

We construct a group K_n with properties similar to infinite Coxeter groups. In particular, it has a geometric representation featuring hyperplanes and simplicial chambers. The generators of K_n are given by 2-element subsets of {0, .., n}.…

Let $K$ be a field and $G$ be a group of its automorphisms. If $G$ is precompact then $K$ is a generator of the category of smooth (i.e. with open stabilizers) $K$-semilinear representations of $G$. There are non-semisimple smooth…

In [Frobenius1896] it was shown that many important properties of a finite group could be examined using formulas involving the character ratios of group elements, i.e., the trace of the element acting in a given irreducible representation,…