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Anton Nazarov

  1. Affine.m - Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras.

    Tue, 07/26/2011 - 15:01 — SomNambul
    Authors: Anton Nazarov
    Subjects: Representation Theory
    Abstract

    In this paper we present Affine.m - program for computations in
    representation theory of finite-dimensional and affine Lie algebras and
    describe implemented algorithms. Algorithms are based upon the properties of
    weights and Weyl symmetry. The most important problems for us are the ones,
    concerning computation of weight multiplicities in irreducible and Verma
    modules, branching of representations and tensor product decomposition. These
    problems have numerous applications in physics and we provide some examples of
    these applications.

  2. Recursive algorithms, branching coefficients and applications.

    Mon, 07/05/2010 - 15:01 — SomNambul
    Authors: Vladimir Lyakhovsky, Anton Nazarov
    Subjects: Representation Theory
    Abstract

    Recurrent relations for branching coefficients in affine Lie algebras
    integrable highest weight modules are studied. The decomposition algorithm
    based on the injection fan technique is adopted to the situation where the Weyl
    denominator becomes singular with respect to a reductive subalgebra. We study
    some modifications of the injection fan technique and demonstrate that it is
    possible to define the "subtracted fans" that play the role similar to the
    original ones. Possible applications of subtracted fans in CFT models are
    considered.

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