Related papers: Spherical representation spaces of quivers
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.
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…
We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.
We systematically determine the regular representations, quivers and representation type of all liftings of two-dimensional quantum linear spaces.
We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…
We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.
In this paper we classify all the quivers and corresponding dimension vectors having a smooth space of semisimple representation classes. The result is that these quiver settings can be reduced via some specific reduction steps to 3 simple…
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
The classical construction of representations of quivers enables us to consider linear maps between several vector spaces. The mixed representations of quivers helps us to work with linear maps as well as bilinear forms on several vector…
Let $n \geq 2$. We introduce the notion of $n$-representations of quivers, and we explicitly provide concrete examples of $2$-representations of quivers. We establish the categories of $n$-representations and investigate kernels and…
Stability conditions play an important role in the study of representations of a quiver. In the present paper, we study semistable representations of quivers. In particular, we describe the slopes of semistable representations of a tame…
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…
The notion of mixed representations of quivers can be derived from ordinary quiver representations by considering the dual action of groups on "vertex" vector spaces together with the usual action. A generating system for the algebra of…
We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
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 definition of the notion of spherical varieties in the world of complex supervarieties with actions of algebraic supergroups. A characterization of affine spherical supervarieties is given which generalizes a characterization in…
We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.
Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…