Related papers: Type A quiver loci and Schubert varieties

We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. As a by-product, we give a counterexample…

We explain that the Pl\"ucker relations provide the defining equations of the thick flag manifold associated to a Kac-Moody algebra. This naturally transplant the result of Kumar-Mathieu-Schwede about the Frobenius splitting of thin flag…

In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on…

Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild…

We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field. We obtain a new proof of the following result due to Xiao and Zhu: the…

We formulate and prove examples of a conjecture which describes the W-algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine…

The intersection cohomologies of closures of nilpotent orbits of linear (respectively, cyclic) quivers are known to be described by Kazhdan-Lusztig polynomials for the symmetric group (respectively, the affine symmetric group). We explain…

We characterize complete intersection matrix Schubert varieties, generalizing the classical result on one-sided ladder determinantal varieties. We also give a new proof of the F-rationality of matrix Schubert varieties. Although it is known…

We define an integral form of shifted quantum affine algebras of type $A$ and construct Poincar\'e-Birkhoff-Witt-Drinfeld bases for them. When the shift is trivial, our integral form coincides with the RTT integral form. We prove that these…

We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy's Durfee square identity to multipartitions. We…

It is a classical result that the set $K\backslash G /B$ is finite, where $G$ is a reductive algebraic group over an algebraically closed field with characteristic not equal to two, $B$ is a Borel subgroup of $G$, and $K = G^{\theta}$ is…

Let Q be a Dynkin quiver of type A. The bounded derived category of the path algebra of Q has an autoequivalence given by the composition of the Auslander-Reiten translate and the square of the shift functor. We classify the maximal rigid…

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…

Generalized flag manifolds endowed with the Bruhat-Poisson bracket are compact Poisson homogeneous spaces, whose decompositions in symplectic leaves coincide with their stratifications in Schubert cells. In this note it is proved that the…

A normal variety $X$ is called $H$-spherical for the action of the complex reductive group $H$ if it contains a dense orbit of some Borel subgroup of $H$. We resolve a conjecture of Hodges--Yong by showing that their spherical permutations…

We construct Nakajima's quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy's) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into…

Let $\Bbbk$ be an algebraically closed field, $Q$ a finite quiver, and denote by $\mathop{\mathrm{rep}}_Q^{\mathbf{d}}$ the affine $\Bbbk$-scheme of representations of $Q$ with a fixed dimension vector ${\mathbf{d}}$. Given a representation…

Consider a compact Lie group and a closed subgroup. Generalizing a result of Klyachko, we give a necessary and sufficient criterion for a coadjoint orbit of the subgroup to be contained in the projection of a given coadjoint orbit of the…

We determine explicitly the irreducible components of the singular locus of any Schubert variety for GL_n(K), K being an algebraically closed field of arbitrary characteristic. We also describe the generic singularities along these…

We show that Zamolodchikov dynamics of a recurrent quiver has zero algebraic entropy only if the quiver has a weakly subadditive labeling, and conjecture the converse. By assigning a pair of generalized Cartan matrices of affine type to…