相关论文: Coefficient Quivers, $\mathbb{F}_1$-Representation…

We study the essential dimension of representations of a fixed quiver with given dimension vector. We also consider the question of when the genericity property holds, i.e., when essential dimension and generic essential dimension agree. We…

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…

Kempf [1976] studied proper, G-equivariant maps from equivariant vector bundles over flag manifolds to G-representations V, which he called _collapsings_. We give a simple formula for the G-equivariant cohomology class on V,…

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…

The representations of dimension vector $\alpha$ of the quiver Q can be parametrised by a vector space $R(Q,\alpha)$ on which an algebraic group $\Gl(\alpha)$ acts so that the set of orbits is bijective with the set of isomorphism classes…

We categorify the action of $U_q(\mathfrak{gl}_{1|1})$ on the tensor product of its vector representations $(\mathbb{C}^{1|1})^{\otimes N}$. The generators $E$ and $F$ are represented by Fourier-Mukai functors between the derived categories…

Let (G,d) be a first order differential *-calculus on a *-algebra A. We say that a pair (\pi,F) of a *-representation \pi of A on a dense domain D of a Hilbert space and a symmetric operator F on D gives a commutator representation of G if…

The aim of this note is to understand the injectivity of Feigin's map $\mathbf{F_w}$ by representation theory of quivers, where $\mathbf{w}$ is the word of a reduced expression of the longest element of a finite Weyl group. This is achieved…

We give a graded dimension formula described in terms of combinatorics of Young diagrams and a simple criterion to determine the representation type for the finite quiver Hecke algebras of type $C_{\ell}^{(1)}$.

It is well-known that the intersection multiplicities of Schubert classes in the Grassmanian are Littlewood-Richardson coefficients. We generalize this statement in the context of quiver representations. Here the intersection multiplicity…

We describe the cohomology groups of a homogeneous vector bundle $E$ on any Hermitian symmetric variety $X=G/P$ of ADE type as the cohomology of a complex explicitly described. The main tool is the equivalence between the category of…

Let $Q$ be a quiver of extended Dynkin type $D$. In this first of two papers, we show that the quiver Grassmannian $Gr_e(M)$ has a decomposition into affine spaces for every dimension vector $e$ and every indecomposable representation $M$…

The goal of this paper is to clarify the connection between certain structures from the theory of totally nonnegative Grassmannians, quiver Grassmannians for cyclic quivers and the theory of local models of Shimura varieties. More…

We introduce a double framing construction for moduli spaces of quiver representations. It allows us to reduce certain sheaf cohomology computations involving the universal representation, to computations involving line bundles, making them…

Let Q be a strongly locally finite quiver and denote by rep(Q) the category of locally finite dimensional representations of Q over some fixed field k. The main purpose of this paper is to get a better understanding of rep(Q) by means of…

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 study four dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K\"{a}hler structure. Using intersecting complex toric surfaces, we derive a class of N=1 quivers with charged fundamental matter placed on…

A systematic study of holomorphic gauge invariant operators in general $\mathcal{N}=1$ quiver gauge theories, with unitary gauge groups and bifundamental matter fields, was recently presented in [1]. For large ranks a simple counting…

We count the $\mathbb{F}_q$-rational points of GIT quotients of quiver representations with relations. We focus on two types of algebras -- one is one-point extended from a quiver $Q$, and the other is the Dynkin $A_2$ tensored with $Q$.…

This is an expository paper which has two parts. In the first part, we study quiver varieties of affine $A$-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating…