Weyl's dimension formula for modules of simple inner Lie triple systems

  1. Benito, P. 1
  2. Madariaga, S. 1
  3. Pérez-Izquierdo, J.M. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Algebra

ISSN: 0021-8693

Year of publication: 2012

Volume: 359

Pages: 104-119

Type: Article

DOI: 10.1016/J.JALGEBRA.2012.03.021 SCOPUS: 2-s2.0-84859581435 WoS: WOS:000303297600007 GOOGLE SCHOLAR

More publications in: Journal of Algebra

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Abstract

In 2002, T.L. Hodge and B.J. Parshall . [7] overviewed the representation theory of Lie triple systems (Lts for short). They proved that finite-dimensional modules of Lts in the sense of Harris (1961) . [5] can be described by using involutory modules of their universal enveloping Lie algebra. The main goal of this paper is to explore the dimension of irreducible modules for simple Lts through dimensional formulas based on the remarkable Weyl formula of irreducible modules of simple Lie algebras. The paper also includes the complete classification of one-dimensional modules in arbitrary characteristic. These modules are the infinitesimal analog of symmetric line bundles. © 2012 Elsevier Inc.