Related papers: A Gelfand-MacPherson correspondence for quiver mod…

The literature on maximal torus orbits in the Grassmannian is vast; in this paper we initiate a program to extend this to diagonal subtori. Our main focus is generalizing portions of Kapranov's seminal work on Chow quotient…

We use an equivariant version of the localization formula of Jeffrey and Kirwan to prove a formula for virtual invariants $(\text{DT}$, $\chi_y$, $\text{Ell})$ of critical loci in quotients of linear spaces by actions of reductive algebraic…

Let I be a finite set and CI be the algebra of functions on I. For a finite dimensional C algebra A with \CI contained in A we show that certain moduli spaces of finite dimsional modules are isomorphic to certain Grassmannian (quot-type)…

Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…

For G a complex reductive group and X a smooth projective or convex quasi-projective polarized G-variety we construct a formal map in quantum K-theory from the equivariant quantum K-theory $QK^G(X)$ to the quantum K-theory of the git…

For a finite subgroup G in SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C^3/G. This paper considers the moduli spaces M_\theta, introduced by Kronheimer and further…

In this text, we characterize the representation type of an acyclic quiver by the properties of its associated quiver Grassmannians. This characterization utilizes and extends known results about singular quiver Grassmannians and cell…

Let $G$ be a reductive group over a local field $F$ of characteristic zero, Archimedean or not. Let $X$ be a $G$-space. In this paper we study the existence of generalized Whittaker quotients for the space of Schwartz functions on $X$,…

Moduli spaces of instantons on ALE spaces for classical groups are examples of fixed point sets of involutions on quiver varieties, i.e., $\sigma$-quiver varieties. In 2018 Yiqiang Li considered their equivariant cohomology, and by stable…

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…

For a smooth affine algebraic group $G$ over an algebraically closed field, we consider several two-variables generalizations of the affine Grassmannian $G(\!(t)\!)/G[\![t]\!]$, given by quotients of the double loop group…

We announce an explicit description of the strictly semistable boundary of the GIT moduli space of quintic threefolds. For the natural action of \(\mathrm{SL}(5)\) on \(\mathbb P(\mathrm{Sym}^5\mathbb C^5)\), we classify the 38 boundary…

There is a natural sequence of CY manifolds that are double covers of the projective g dimensional spaces ramified over 2g+2 hyperplanes. We observe that some of them are obtained as quotient of the action of the semi-direct product of g-1…

In this paper we provide some stability criteria for systems of linear subspaces of $V \otimes W$ and for systems of quotient coherent sheaves, using, respectively, the Hilbert-Mumford numerical criterion and moment map. Along the way, we…

We give a description of faces of all codimensions for the cones of weights of rings of semi-invariants of quivers. For a triple flag quiver and faces of codimension 1 this reduces to the result of Knutson-Tao-Woodward on the facets of the…

We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation-finite algebra,…

We prove that a GIT chamber quotient of an affine variety $X=Spec(A)$ by a reductive group $G$, where $A$ is an almost factorial domain, is a Mori dream space if it is projective, regardless of the codimension of the unstable locus. This…

Let $X$ be a variety with an action by an algebraic group $G$. In this paper we discuss various properties of $G$-equivariant $D$-modules on $X$, such as the decompositions of their global sections as representations of $G$ (when $G$ is…

We consider the action of the one-parameter subgroup of the special linear group corresponding to a simple root on Grassmannians and describe the structure of the associated Geometric Invariant Theory (GIT) quotients with respect to…

Given a finite quiver, its double may be viewed as its non-commutative "cotangent" space, and hence is a non-commutative symplectic space. Crawley-Boevey, Etingof and Ginzburg constructed the non-commutative reduction of this space while…