Related papers: Quiver varieties, category O for rational Cheredni…
In this paper, we introduce generalized quiver varieties which include as special cases classical and cyclic quiver varieties. The geometry of generalized quiver varieties is governed by a finitely generated algebra P: the algebra P is…
Given a quiver with potential $(Q,W)$, Kontsevich-Soibelman constructed a Hall algebra on the critical cohomology of the stack of representations of $(Q,W)$. Special cases of this construction are related to work of Nakajima, Varagnolo,…
Drinfeld orbifold algebras deform skew group algebras in polynomial degree at most one and hence encompass graded Hecke algebras, and in particular symplectic reflection algebras and rational Cherednik algebras. We introduce parametrized…
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 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…
In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group $G_4$. In particular, we classify the irreducible finite dimensional representations and compute their characters.
We define a category of planar diagrams whose Grothendieck group contains an integral version of the infinite rank Heisenberg algebra, thus yielding a categorification of this algebra. Our category, which is a q-deformation of one defined…
We study the rational Cherednik algebra attached to the complex reflection group $G(r,1,2)$. Each irreducible representation $S^\lambda$ of $G(r,1,2)$ corresponds to a standard module $\Delta(\lambda)$ for the rational Cherednik algebra. We…
The Zariski closures of the orbits for representations of type A Dynkin quivers under the action of general linear groups (i.e. quiver loci) exhibit a profound connection with Schubert varieties. In this paper, we present a…
Based on a construction by Kashiwara and Rouquier, we present an analogue of the Beilinson- Bernstein localization theorem for hypertoric varieties. In this case, sheaves of differential operators are replaced by sheaves of W-algebras. As a…
In this paper we construct full support character sheaves for stably graded Lie algebras. Conjecturally these are precisely the cuspidal character sheaves. Irreducible representations of Hecke algebras associated to complex reflection…
In this paper we study the combinatorial consequences of the relationship between rational Cherednik algebras of type $G(l,1,n)$, cyclic quiver varieties and Hilbert schemes. We classify and explicitly construct $\mathbb{C}^*$-fixed points…
We provide geometric constructions of modules over the graded Cherednik algebra $\mathfrak{H}^{gr}_\nu$ and the rational Cherednik algebra $\mathfrak{H}^{rat}_\nu$ attached to a simple algebraic group $\mathbb{G}$ together with a pinned…
We study equivalences for category O_p of the rational Cherednik algebras H_p of type G_l(n) = \mu_l^n\rtimes S_n: a highest weight equivalence between O_p and O_{\sigma(p)} for \sigma\in S_l and an action of S_l on a non-empty Zariski open…
We study a connection between the representation theory of the rational Cherednik algebra of type $GL_n$ and the representation theory of the degenerate double affine Hecke algebra (the degenerate DAHA). We focus on an algebra embedding…
In this paper we describe the characters of irreducible objects in category O for the rational Cherednik algebra associated to GL_2(F_p) over an algebraically closed field of positive characteristic p, for any value of the parameter t and…
We consider the algebra of Hecke correspondences (elementary transformations at a single point) acting on the algebraic K-theory groups of the moduli spaces of stable sheaves on a smooth projective surface S. We derive quadratic relations…
We give an alternate presentation of the cyclotomic rational Cherednik algebra, which has the useful feature of compatibility with the Opdam-Dunkl subalgebra. This presentation has a diagrammatic flavor, and it provides a simple explanation…
We prove that the extended Khovanov arc algebras are isomorphic to the basic algebras of anti-spherical Hecke categories for maximal parabolics of symmetric groups. We present these algebras by quiver and relations and provide the full…
We consider irreducible lowest-weight representations of Cherednik algebras associated to certain classes of complex reflection groups in characteristic p. In particular, we study maximal graded submodules of Verma modules associated to…