Related papers: Nest representations of directed graph algebras
We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…
A finite group $G$ admits an {\em oriented regular representation} if there exists a Cayley digraph of $G$ such that it has no digons and its automorphism group is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we extend…
Given a subshift over an arbitrary alphabet, we construct a representation of the associated unital algebra. We describe a criteria for the faithfulness of this representation in terms of the existence of cycles with no exits. Subsequently,…
For a central division algebra $D$, we study a family of representations of $\mathrm{GL}_{k,D}$ (both locally and globally), which can be viewed as analogues of the Speh representations. Locally, we study unique models for these…
The codegree of an irreducible character $\chi$ of a finite group $G$ is defined as $|G:\ker\chi|/\chi(1)$. The codegree graph $\Gamma(G)$ of a finite group $G$ is the graph whose vertices are the prime divisors of $|G|$, where two distinct…
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…
By finding orthogonal representation for a family of simple connected called $\delta$-graphs it is possible to show that $\delta$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form…
Selfdual representations of any group fall into two classes when they are irreducible: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the…
We prove that all finite W-algebras associated with nilpotent elements e in a complex semisimple Lie algebra g have finite-dimensional representations. In order to obtain this result we establish a connection between primitive ideals of…
We give a complete description of the bounded (i.e. norm continuous) unitary representations of the Fr\'echet-Lie algebra of all smooth sections, as well as of the LF-Lie algebra of compactly supported smooth sections, of a smooth Lie…
The genus of projective curves discretely separates decidedly different two variable algebraic relations. So, we can focus on the connected moduli M_g of genus g curves. Yet, modern applications require a data variable (function) on such…
Semialgebraic graphs are graphs whose vertices are points in $\mathbb{R}^d$, and adjacency between two vertices is determined by the truth value of a semialgebraic predicate of constant complexity. We show how to harness polynomial…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)\in E$. A triangular grid graph is a subgraph of a tiling of the plane with…
A dominating set in a graph $G$ is a set $S$ of vertices such that every vertex of $G$ is either in $S$ or is adjacent to a vertex in $S$. Nordhaus-Gaddum inequailties relate a graph $G$ to its complement $\bar{G}$. In this spirit Wagner…
We determine which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero. This…
Given an $n$-vertex graph $G$, let $\hom (G)$ denote the size of a largest homogeneous set in $G$ and let $f(G)$ denote the maximal number of distinct degrees appearing in an induced subgraph of $G$. The relationship between these…
Let $S$ be a unital associative ring and $S[t;\sigma,\delta]$ be a skew polynomial ring, where $\sigma$ is an injective endomorphism of $S$ and $\delta$ a left $\sigma$-derivation. For each $f\in S[t;\sigma,\delta]$ of degree $m>1$ with a…
We prove that if $ T $ is a semi-special tree that is not special, then there exists a graph $ G $, formed as an inflation of a sparse $ T $-graph, such that for any special tree $ S $, $ G $ is not a subdivision of an inflation of an…
We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because…
We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), U_q(gl(n)) or U_q(gl(m|n)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain. In…