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Quantized symplectic actions and W -algebras
With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universalExpand
Etingof conjecture for quantized quiver varieties
We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing and provide an exactExpand
Supports of simple modules in cyclotomic Cherednik categories O
The goal of this paper is to compute the supports of simple modules in the categories $\mathcal{O}$ for the rational Cherednik algebras associated to groups $G(\ell,1,n)$. For this we compute someExpand
Proof of the Knop conjecture
In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoids are equivariantly isomorphic. We also state and prove a uniquenessExpand
Finite-dimensional representations of W-algebras
W-algebras of finite type are certain finitely generated associative algebras closely related to the universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture ofExpand
Isomorphisms of quantizations via quantization of resolutions
Abstract In this paper, we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from the representation theoretic perspective and arise as quantizationsExpand
Deformations of symplectic singularities and Orbit method for semisimple Lie algebras
We classify filtered quantizations of conical symplectic singularities and use this to show that all filtered quantizations of symplectic quotient singularities are spherical Symplectic reflectionExpand
On uniqueness of tensor products of irreducible categorifications
In this paper, we propose an axiomatic definition for a tensor product categorification. A tensor product categorification is an abelian category with a categorical action of a Kac–Moody algebraExpand
Representations of Rational Cherednik algebras with minimal support and torus knots
We obtain several results about representations of rational Cherednik algebras, and discuss their applications. Our first result is the Cohen-Macaulayness property (as modules over the polynomialExpand
Uniqueness property for spherical homogeneous spaces
Let G be a connected reductive group. Recall that a homogeneous G-space X is called spherical if a Borel subgroup B ⊂ G has an open orbit on X. To X one assigns certain combinatorial invariants: theExpand