We study algebraic actions of finite groups of quiver automorphisms on moduli spaces of quiver representations. We decompose the fixed loci using group cohomology and we give a modular interpretation of each component. As an application, we construct branes in hyperkähler quiver varieties, as fixed loci of such actions.

The authors develop an algorithm for a field theoretical implementation of mirror symmetry. This is based on the so-called quiver representation certain $N=1$ supersymmetric theories and non-abelian generalization piecewise dualization three-dimensional abelian theories. Extensions this local field-theoretic operations to non-supersymmetric are expected.

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two can be added or composed. Algebraically, identities modelled noncommutative polynomials such proves that the polynomial corresponding to lies ideal generated identities. In order prove an identity, however, just membership is ...

We construct Nakajima’s quiver varieties of type A in terms of affine Grassmannians of type A. This gives a compactification of quiver varieties and a decomposition of affine Grassmannians into a disjoint union of quiver varieties. Consequently, singularities of quiver varieties, nilpotent orbits and affine Grassmannians are the same in type A. The construction also provides a geometric framewo...

Quivers of finite mutation type have been classified recently in [4]. Main examples of these quivers are the quivers associated with triangulations of surfaces as introduced in [5]. They are also closely related to the representation theory of algebras [1]. In this paper, we study structural properties of finite mutation type quivers. We determine a class of subquivers, which we call basic quiv...

We introduce the principal representation category O ( G ) of reductive algebraic groups with Frobenius maps. When k is an algebraically closed field characteristic 0, we put forward a conjecture that this highest weight and provide some evidences conjecture. also study certain kind bound quiver algebras whose representations are related to .

Inspired by Cachazo, Katz and Vafa (“Geometric transitions and N = 1 quiver theories” (hep-th/0108120)), we examine representations of “N = 1 quivers” arising from string theory. We derive some mathematical consequences of the physics, and show that these results are a natural extension of Gabriel’s ADE theorem. Extending the usual ADE case that relates quiver representations to curves on surfa...

Given a basic K-coalgebra C, we study the left Gabriel-valued quiver (CQ,Cd) of C by means of irreduciblemorphisms between indecomposable injective leftC-comodules and by means of the powers rad of the radical rad of the category C-inj of the socle-finite injective left C-comodules. Connections between the valued quiver (CQ,C d) of C and the valued quiver (CQ,Cd) of a colocalization coalgebra q...

In this paper we detail the lattice constructions of several classes of supersymmetric quiver gauge theories in two and three Euclidean spacetime dimensions possessing exact supersymmetry at finite lattice spacing. Such constructions are obtained through the methods of topological twisting and geometric discretization of Euclidean Yang-Mills theories with eight and sixteen supercharges in two a...

In a previous paper the authors have attached to each Dynkin quiver an associative algebra. The definition is categorical and the algebra is used to construct desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain graded Nakajima quiver...