Related papers: $D_n$ Dynkin quiver moduli spaces
Exceptional modules are tree modules. A tree module usually has many tree bases and the corresponding coefficient quivers may look quite differently. The aim of this note is to introduce a class of exceptional modules which have a…
In this paper we propose a special class of 3-algebras, called double-symplectic 3-algebras. We further show that a consistent contraction of the double-symplectic 3-algebra gives a new 3-algebra, called an N=4 three-algebra, which is then…
We use the theory of differential tensor algebras and their modules to produce explicit representations of extended Dynkin quivers.
A distinctive duality present in 3d $\mathcal{N}=4$ theories is the 3d mirror symmetry. Under this duality, the Coulomb (Higgs) branch of one theory corresponds to the Higgs (Coulomb) branch of its mirror dual. This paper is divided into…
We describe a method for an explicit determination of indecomposable preprojective and preinjective representations for extended Dynkin quivers by vector spaces and matrices. This method uses tilting theory and the explicit knowledge of…
After reviewing D-branes as conjugacy classes and various charge quantizations (modulo $k$) in WZW model, we develop the classification and systematic construction of all possible untwisted D-branes in Lie groups of A-D-E series. D-branes…
We develop the theory of associating moduli spaces with nice geometric properties to arbitrary Artin stacks generalizing Mumford's geometric invariant theory and tame stacks.
We study the moduli space of 3d $\mathcal{N}=4$ quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise…
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual…
We construct moduli spaces of representations of quivers over arbitrary schemes and show how moduli spaces of pointed curves of genus zero like the Grothendieck-Knudsen moduli spaces $\overline{M}_{0,n}$ and the Losev-Manin moduli spaces…
Exceptional sequences are certain ordered sequences of quiver representations. We introduce a class of objects called strand diagrams and use this model to classify exceptional sequences of representations of a quiver whose underlying graph…
We consider a class of super-conformal beta-deformed N=1 gauge theories dual to string theory on $AdS_5 \times X$ with fluxes, where $X$ is a deformed Sasaki-Einstein manifold. The supergravity backgrounds are explicit examples of…
Let $C$ be an arrangement of affine hyperplanes in a complex affine space $X$, $D$ the ring of algebraic differential operators on $X$. We define a category of quivers associated with $C$. A quiver is a collection of vector spaces, attached…
The connection between quiver gauge theories and dimer models has been well studied. It is known that the matter fields of the quiver gauge theories can be represented using the perfect matchings of the corresponding dimer model.We…
We study the singularities of normalized R-matrices between arbitrary simple modules over the quantum loop algebra of type ADE in Hernandez--Leclerc's level-one subcategory using equivariant perverse sheaves, following the previous works by…
This is the third in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin…
Let $A$ be the path algebra of a quiver of Dynkin type $\mathbb{A}_n$. The module category $\text{mod}\,A$ has a combinatorial model as the category of diagonals in a polygon $S$ with $n+1$ vertices. The recently introduced notion of almost…
Exceptional sequences are important sequences of quiver representations in the study of representation theory of algebras. They are also closely related to the theory of cluster algebras and the combinatorics of Coxeter groups. We…
We study modules for the divided power algebra $D$ in a single variable over a commutative noetherian ring $k$. Our first result states that $D$ is a coherent ring. In fact, we show that there is a theory of Gr\"obner bases for finitely…
We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We focus on the strange duality map $SD_{c_n^r,d}$ which involves the moduli space of rank $r$ sheaves with trivial first Chern class and second Chern class $n$, and the…