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Quantized symplectic actions and W -algebras

- I. Losev
- Mathematics
- 20 July 2007

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 universal… Expand

Etingof conjecture for quantized quiver varieties

- R. Bezrukavnikov, I. Losev
- Mathematics
- 6 September 2013

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 exact… Expand

Supports of simple modules in cyclotomic Cherednik categories O

- I. Losev
- Mathematics
- 1 September 2015

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 some… Expand

Proof of the Knop conjecture

- I. Losev
- Mathematics
- 19 December 2006

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 uniqueness… Expand

Finite-dimensional representations of W-algebras

- I. Losev
- Mathematics
- 7 July 2008

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 of… Expand

Isomorphisms of quantizations via quantization of resolutions

- I. Losev
- Mathematics
- 15 October 2010

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 quantizations… Expand

Deformations of symplectic singularities and Orbit method for semisimple Lie algebras

- I. Losev
- Mathematics
- 2 May 2016

We classify filtered quantizations of conical symplectic singularities and use this to show that all filtered quantizations of symplectic quotient singularities are spherical Symplectic reflection… Expand

On uniqueness of tensor products of irreducible categorifications

- I. Losev, B. Webster
- Mathematics
- 6 March 2013

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 algebra… Expand

Representations of Rational Cherednik algebras with minimal support and torus knots

- P. Etingof, E. Gorsky, I. Losev
- Mathematics
- 11 April 2013

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 polynomial… Expand

Uniqueness property for spherical homogeneous spaces

- I. Losev
- Mathematics
- 19 March 2007

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: the… Expand

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