Related papers: Dimension expanders via quiver representations
We present two approaches, one homological and the other simplicial, for the investigation of dimension quotients of groups. The theory is illustrated, in particular, with a conceptual discussion of the fourth and fifth dimension quotients.
The evolution of human intelligence led to the huge amount of data in the information space. Accessing and processing this data helps in finding solutions to applied problems based on finite-dimensional models. We argue, that formally, such…
We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some…
Stretching the parameters of a Littlewood-Richardson coefficient of value 2 by a factor of n results in a coefficient of value n+1. We give a geometric proof of a generalization for representations of quivers.
We discuss an explicit field theory construction of three dimensional mirrors for a large sub-class of quiver gauge theories involving unitary and special unitary gauge nodes with matter in fundamental and bifundamental representations. For…
It is well-known that a quiver Q of type A_n is representation-finite, and that its indecomposable representations are thin (all Jordan-Hoelder multiplicities are 0 or 1). By now, various methods of proof are known. The aim of this note is…
We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of Schoen and Shkredov. We obtain bounds for the ratios between…
We investigate the Schr\"odinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.
We consider new ways of obtaining series and integral representations for master integrals arising in the process of matching of QCD to NRQCD. The latter results are exact in space-time dimension $d$. In addition, we discuss series…
In this paper we study the three-dimensional analogue of the relation between the irrationality exponent of a real number and the growth of its regular continued fraction partial quotients. As a multidimensional generalisation of continued…
We explicitly construct and list all unitary superconformal multiplets, along with their index contributions, in five and six dimensions. From this data, we uncover various unifying themes in the representation theory of five- and…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles
We define a pair of simple combinatorial operations on subshifts, called existential and universal extensions, and study their basic properties. We prove that the existential extension of a sofic shift by another sofic shift is always…
A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.
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 present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory…
We introduce a notion of global dimension for a triangulated category relative to a compact silting object. We prove that the finiteness of this dimension is an intrinsic property of the triangulated category itself and, therefore,…
We present a new construction of high dimensional expanders based on covering spaces of simplicial complexes. High dimensional expanders (HDXs) are hypergraph analogues of expander graphs. They have many uses in theoretical computer…