Search for dissertations about: "highest weight representation"

Showing result 1 - 5 of 7 swedish dissertations containing the words highest weight representation.

  2. 1. Exercising Mathematical Competence: Practising Representation Theory and Representing Mathematical Practice

    Author : Anna Ida Säfström; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; SAMHÄLLSVETENSKAP; SOCIAL SCIENCES; Mathematical competence; exercising competencies; young children; whole number arithmetic; tertiary level; proving; highest weight representation; tensor product decomposition; skew-symmetric matrix; moment map; infinite dimensional unitary representation; highest weight representation;

    Abstract : This thesis assembles two papers in mathematics and two papers in mathematics education. In the mathematics part, representation theory is practised. Two Clebsch-Gordan type problems are addressed. READ MORE

  4. 2. Tensor Products of Highest Weight Representations and Skew-Symmetric Matrix Equations A+B+C=0

    Author : Ida Säfström; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Highest weight respresentation; tensor product decomposition; orthogonal algebra; skew-symmetric matrix; Horn’s conjecture; moment map; coadjoint orbit; flag manifold; general linear algebra; infinite dimensional unitary representation; general linear algebra;

    Abstract : The question of characterizing the eigenvalues for the sum of two Hermitian matrices, was solved in 1999, after almost a century of efforts. The saturation conjecture for GL_C(n) was proven by Knutson and Tao, filling in the last gap in Horn’s conjecture. READ MORE

  5. 3. Simple Modules over Lie Algebras

    Author : Jonathan Nilsson; Volodymyr Mazorchuk; Erhard Neher; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Lie algebra; Representation; Simple module; Non-weight module; Classification; Construction; Mathematics; Matematik;

    Abstract : Simple modules are the elemental components in representation theory for Lie algebras, and numerous mathematicians have worked on their construction and classification over the last century. This thesis consists of an introduction together with four research articles on the subject of simple Lie algebra modules. READ MORE

  6. 4. Multivariable Orthogonal Polynomials as Coupling Coefficients for Lie and Quantum Algebra Representations

    Author : Hjalmar Rosengren; Matematik (naturvetenskapliga fakulteten); []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; higher order Hankel form; Wigner symbol; quadratic algebra; Clebsch-Gordan coefficient; quantum group; Lie group; highest weight representation; multivariable orthogonal and biorthogonal polynomials; multivariable hypergeometric and basic hypergeometric functions; algebraisk topologi; Geometry; Geometri; algebraic topology;

    Abstract : The main topic of the thesis is the connection between representation theory and special functions. We study matrix elements, coupling coefficient, and recoupling coefficients for the simplest Lie and quantum groups. READ MORE

  7. 5. Irreducible Representations of Quantum Affine Algebras

    Author : Jesper Thorén; Matematik (naturvetenskapliga fakulteten); []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Number Theory; Matematik; Mathematics; quantum evaluation modules; highest weight representations; quantum Yang-Baxter equation; quantum affine algebras; quantum groups; comultiplication; Hopf algebras; affine Lie algebras; field theory; algebraic geometry; algebra; group theory; Talteori; fältteori; algebraisk geometri; gruppteori;

    Abstract : We construct finite-dimensional representations of the quantum affine algebra associated to the simple finite-dimensional Lie algebra sl(n+1). The module structure is defined on the vector space tensor product of the fundamental representations of the quantum affine algebra. READ MORE