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Antun Milas

  1. Lattice construction of logarithmic modules for certain vertex algebras.

    Tue, 09/29/2009 - 15:21 — SomNambul
    Authors: Drazen Adamovic, Antun Milas
    Subjects: Quantum Algebra
    Abstract

    A general method for constructing logarithmic modules in vertex operator
    algebra theory is presented. By utilizing this approach, we give explicit
    vertex operator construction of certain indecomposable and logarithmic modules
    for the triplet vertex algebra W(p) and for other subalgebras of lattice vertex
    algebras and their N=1 super extensions.

  2. On W-algebras associated to (2,p) minimal models and their representations.

    Fri, 08/28/2009 - 23:56 — SomNambul
    Authors: Drazen Adamovic, Antun Milas
    Subjects: Quantum Algebra
    Abstract

    For every odd p \geq 3, we investigate representation theory of the vertex
    algebra WW_{2,p} associated to (2,p) minimal models for the Virasoro algebras.
    We demonstrate that vertex algebras WW_{2,p} are C_2-cofinite and irrational.
    Complete classification of irreducible representations for WW_{2,3} is
    obtained, while the classification for p>3 is subject to certain constant term
    identities. These identities can be viewed as "logarithmic deformations" of
    Dyson's constant term identities, and are of independent interest.

  3. Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A,D,E.

    Fri, 08/28/2009 - 23:56 — SomNambul
    Authors: Antun Milas, Corina Calinescu, James Lepowsky
    Subjects: Quantum Algebra
    Abstract

    Generalizing some of our earlier work, we prove natural presentations of the
    principal subspaces of the level one standard modules for the untwisted affine
    Lie algebras of types A, D and E, and also of certain related spaces. As a
    consequence, we obtain a canonical complete set of recursions (q-difference
    equations) for the (multi-)graded dimensions of these spaces, and we derive
    their graded dimensions. Our methods are based on intertwining operators in
    vertex operator algebra theory.

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