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Ivan Losev

  1. Classification of finite dimensional irreducible modules over W-algebras.

    Wed, 02/29/2012 - 15:01 — SomNambul
    Authors: Ivan Losev, Victor Ostrik
    Subjects: Representation Theory
    Abstract

    Finite W-algebras are certain associative algebras arising in Lie theory.
    Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our
    base field is algebraically closed and of characteristic 0) and its nilpotent
    element e. In this paper we classify finite dimensional irreducible modules
    with integral central character over W-algebras.

  2. Completions of symplectic reflection algebras.

    Tue, 01/05/2010 - 16:01 — SomNambul
    Authors: Ivan Losev
    Subjects: Representation Theory
    Abstract

    In this paper we study the structure of completions of symplectic reflection
    algebras. Our results provides a reduction to smaller algebras. We apply this
    reduction to the study of two-sided ideals and Harish-Chandra bimodules.

  3. Poisson traces and D-modules on Poisson varieties.

    Thu, 08/27/2009 - 13:23 — SomNambul
    Authors: Pavel Etingof, Travis Schedler, Ivan Losev
    Subjects: Symplectic Geometry
    Abstract

    To every Poisson algebraic variety X over an algebraically closed field of
    characteristic zero, we canonically attach a right D-module M(X) on X. If X is
    affine, solutions of M(X) in the space of algebraic distributions on X are
    Poisson traces on X, i.e., distributions invariant under Hamiltonian flows.
    When X has finitely many symplectic leaves, we prove that M(X) is holonomic.
    Thus, when X is affine and has finitely many symplectic leaves, the space of
    Poisson traces on X is finite-dimensional.

  4. Poisson traces and D-modules on Poisson varieties.

    Thu, 08/27/2009 - 13:23 — SomNambul
    Authors: Pavel Etingof, Travis Schedler, Ivan Losev
    Subjects: Symplectic Geometry
    Abstract

    To every Poisson algebraic variety X over an algebraically closed field of
    characteristic zero, we canonically attach a right D-module M(X) on X. If X is
    affine, solutions of M(X) in the space of algebraic distributions on X are
    Poisson traces on X, i.e., distributions invariant under Hamiltonian flows.
    When X has finitely many symplectic leaves, we prove that M(X) is holonomic.
    Thus, when X is affine and has finitely many symplectic leaves, the space of
    Poisson traces on X is finite-dimensional.

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