Related papers: Symplectic reflection algebras
We give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products (with parameter t=0) and the derived category of coherent…
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the…
We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in…
In this paper we introduce the notion of twisted symplectic reflection algebras and describe the category of representations of such an algebra associated to a non-faithful G-action in terms of those for faithful actions of G.
Symplectic resolutions are an exciting new frontier of research in representation theory. One of the most fascinating aspects of this study is symplectic duality: the observation that these resolutions come in pairs with matching…
This paper surveys the representation theory of rational Cherednik algebras. We also discuss the representations of the spherical subalgebras. We describe in particular the results on category O. For type A, we explain relations with the…
We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic…
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
In this paper we study derived equivalences for Symplectic reflection algebras. We establish a version of the derived localization theorem between categories of modules over Symplectic reflection algebras and categories of coherent sheaves…
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…
Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type ADE can be recovered from the data of the corresponding…
We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
The current article is a short survey on the theory of Hecke algebras, and in particular Kazhdan-Lusztig theory, and on the theory of symplectic reflection algebras, and in particular rational Cherednik algebras. The emphasis is on the…
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…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
We investigate the Poisson geometry of the Marsden-Weinstein reductions of the moment map associated to the cotangent bundle of the space of representations of a quiver. We show that the stratification by representation type equals the…
We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the $R$-matrix associated to the $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We develop a form…