Related papers: Derived Representation Schemes and Nakajima Quiver…
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties. This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras…
We study preprojective algebras of graphs and their relationship to module categories over representations of quantum SL(2). As an application, ADE quiver varieties of Nakajima are shown to be subvarieties of the variety of representations…
We are concerned with relating derived categories of all modules of two dual Koszul algebras defined by a locally bounded quiver. We first generalize the well known Acyclic Assembly Lemma and formalize an old method of extending a functor…
This paper aims to study graded modules over a graded algebra $\La$ given by a locally finite quiver with homogeneous relations. By constructing a graded Nakayama functor, we discover a novel approach to establish Auslander-Reiten formulas,…
In this paper we provide a systematic way of producing representations of cohomological, K-theoretical and categorified Hall algebras, and study the output of our construction in several cases. We thus recover and categorify in a unified…
We construct geometric categorical Lie algebra actions on the derived category of coherent sheaves on Nakajima quiver varieties. These actions categorify Nakajima's construction of Kac-Moody algebra representations on the K-theory of quiver…
Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…
Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or…
We study the behavior of representation varieties of quivers with relations under the operation of node splitting. We show how splitting a node gives a correspondence between certain closed subvarieties of representation varieties for…
We study the moduli space of twisted quasimaps from a fixed smooth projective curve to a Nakajima's quiver variety and the moduli space of $\delta$-stable framed twisted quiver bundles with moment map relations. We show that they carry…
We describe derived moduli functors for a range of problems involving schemes and quasi-coherent sheaves, and give cohomological conditions for them to be representable by derived geometric n-stacks. Examples of problems represented by…
We construct stable envelopes in equivariant elliptic cohomology of Nakajima quiver varieties. In particular, this gives an elliptic generalization of the results of arXiv:1211.1287. We apply them to the computation of the monodromy of…
We show that the category of representations of the Euclidean group of orientation-preserving isometries of two-dimensional Euclidean space is equivalent to the category of representations of the preprojective algebra of infinite type A. We…
We define a derived enhancement of the hyperquot scheme (also known as nested Quot scheme), which classically parametrises flags of quotients of a perfect coherent sheaf on a projective scheme. We prove it is representable by a derived…
In the context of varieties of representations of arbitrary quivers, possibly carrying loops, we define a generalization of Lusztig Lagrangian subvarieties. From the combinatorial study of their irreducible components arises a structure…
Dynamical systems often admit geometric properties that must be taken into account when studying their behaviour. We show that many such properties can be encoded by means of quiver representations. These properties include classical…
In this paper we determine the derived representation type of quadratic string algebras and we prove that every derived tame quadratic string algebra whose quiver has cycles is derived equivalent to some skewed-gentle algebra.
We have two constructions of the level-$(0,1)$ irreducible representation of the quantum toroidal algebra of type $A$. One is due to Nakajima and Varagnolo-Vasserot. They constructed the representation on the direct sum of the equivariant…
We relate two apparently different bases in the representations of affine Lie algebras of type A: one arising from statistical mechanics, the other from gauge theory. We show that the two are governed by the same combinatorics and therefore…