相关论文: Orthogonal and symplectic bundles on curves and qu…

This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…

We prove that the forgetful morphism from the moduli space of orthogonal bundles to the moduli space of vector bundles over a smooth curve is an embedding. Our proof relies on an explicit description of a set of generators for the…

Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of $\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of quadric…

This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.

In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The…

We embed several copies of the derived category of a quiver and certain line bundles in the derived category of an associated moduli space of representations, giving the start of a semiorthogonal decomposition. This mirrors the…

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of…

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…

In this article, we study the smoothness of the moduli space of finite quiver vector bundles over the smooth complex projective curves.

We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.

We introduce the notion of a Nakajima bundle representation. Given a labelled quiver and a variety or manifold $X$, such a representation involves an assignment of a complex vector bundle on $X$ to each node of the doubled quiver; to the…

We review the theory of quiver bundles over a K\"ahler manifold, and then introduce the concept of generalized quiver bundles for an arbitrary reductive group G. We first study the case when G=O(V) or Sp(V), interpreting them as orthogonal…

This paper studies the geometric and algebraic aspects of the moduli spaces of quivers of fence type. We first provide two quotient presentations of the quiver varieties and interpret their equivalence as a generalized Gelfand-MacPherson…

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 analyze the local structure of the moduli space of semi-stable bundles on a curve. In particular, a complete description of the local structure is given in the rank 2 case. We obtain as a corollary of this analysis new results about the…

A symplectic or orthogonal bundle $V$ of rank $2n$ over a curve has an invariant $t(V)$ which measures the maximal degree of its isotropic subbundles of rank $n$. This invariant $t$ defines stratifications on moduli spaces of symplectic and…

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…

It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…