Sökning: "Verma modules"

Hittade 4 avhandlingar innehållade orden Verma modules.

1. 1. Studies on boundary values of eigenfunctions on spaces of constant negative curvature

   Författare :Pierre Bäcklund; Andreas Juhl; Andreas Strömbergsson; Genkai Zhang; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Hyperbolic space; anti de Sitter space; spectral geometry; scattering theory; analysis on real and complex Lie groups; intertwining operators; Verma modules; analysis on homogeneous spaces; conformal differential geometry; Selberg zeta functions; Algebra; geometry and mathematical analysis; Algebra; geometri och analys;

   Sammanfattning : This thesis consists of two papers on the spectral geometry of locally symmetric spaces of Riemannian and Lorentzian signature. Both works are concerned with the idea of relating analysis on such spaces to structures on their boundaries.The first paper is motivated by a conjecture of Patterson on the Selberg zeta function of Kleinian groups. LÄS MER

3. 2. Tensor Products on Category O and Kostant's Problem

   Författare :Johan Kåhrström; Volodymyr Mazorchuk; Henning Haahr Andersen; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Semi-simple Lie algebras; Tensor products; Kostant s problem; Primitive quotients; MATHEMATICS; MATEMATIK;

   Sammanfattning : This thesis consists of a summary and three papers, concerning some aspects of representation theory for complex finite dimensional semi-simple Lie algebras with focus on the BGG-category O.Paper I is motivated by the many useful properties of functors on category O given by tensoring with finite dimensional modules, such as projective functors and translation functors. LÄS MER

4. 3. On Vertex Operator Algebras of Affine Type at Admissible Levels

   Författare :Thomas Edlund; Matematik (naturvetenskapliga fakulteten); []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Vertex operator algebras; Kac-Moody algebras; Ore localization; Admissible levels; Singular vectors; Intertwining operators;

   Sammanfattning : The main purpose of this thesis is the study of the structure and representation theory of simple vertex operator algebras (VOAs) of affine type at admissible levels. To do this, it is crucial to obtain knowledge of the singular vectors which generate the maximal submodules, with respect to which these VOAs appear as irreducible quotients, and therefore a substantial part of the text is devoted to this matter. LÄS MER

5. 4. Structure and representations of certain classes of infinite-dimensional algebras

   Författare :Brendan Frisk Dubsky; Volodymyr Mazorchuk; Martin Herschend; Rolf Farnsteiner; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; infinite-dimensional algebras; representation theory; category O; koszul; koszulity; injections; dihedral; preprojective; young lattice; Mathematics; Matematik;

   Sammanfattning : We study several infinite-dimensional algebras and their representation theory. In Paper I, we study the category O for the (centrally extended) Schrödinger Lie algebra, which is an analogue of the classical BGG category O. We decompose the category into a direct sum of "blocks", and describe Gabriel quivers of these blocks. LÄS MER