Related papers: Kac's Theorem for equipped graphs and for maximal …
We propose a definition of expander representations of quivers, generalizing dimension (or linear algebra) expanders, as a qualitative refinement of slope stability. We prove existence of uniform expander representations for any wild quiver…
We give a criterion for the Kac conjecture asserting that the free term of the polynomial counting the absolutely indecomposable representations of a quiver over a finite field of given dimension coincides with the corresponding root…
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
A representation theory of the quantized Poincar\'e ($\kappa$-Poincar\'e) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the non-deformed Poincar\'e algebra. A…
A conjecture of Kac states that the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field with given dimension vector has positive coefficients and furthermore that its constant term is…
We give a general formula for the equivariant complex $K$-theory $K_G^*(V)$ of a finite dimensional real linear space $V$ equipped with a linear action of a compact group $G$ in terms of the representation theory of a certain double cover…
We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this…
We review known linear and matrix generalizations of Hall's classic ``marriage theorem'' and K\H{o}nig's theorem on partial matchings in bipartite graphs, and relate them to linear and matrix generalizations of Dilworth's theorem about…
The First and Second Representation Theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the…
In this paper, we generalize the notions of perfect matchings, perfect 2-matchings to perfect k-matchings and give a necessary and sufficient condition for existence of perfect k-matchings. For bipartite graphs, we show that this k-matching…
We study in this paper the maximal version of the coarse Baum-Connes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to…
The vertices of a $k$-token graph of a graph $G$ correspond to $k$ indistinguishable tokens placed on $k$ different vertices of $G$. Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…
A universal representation theorem is derived that shows any graph is the intersection graph of one chordal graph, a number of co-bipartite graphs, and one unit interval graph. Central to the the result is the notion of the clique cover…
In this paper we prove a generalized version of Hall's theorem for hypergraphs. More precisely, let H be a k-uniform k- partite hypergraph with some ordering on parts as V1, V2,..., Vk. such that the subhypergraph generated on union of V1,…
We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other "rank functors" for a…
A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…