• Multiplicity formulas for finite dimensional and generalized principal series representations

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/106/04/0379-0401

    • Keywords

       

      Reductive Lie algebra and subgroup; maximal compact group; weight; partition function; multiplicity; generalized principal series

    • Abstract

       

      The article presents two results. (1) Let a be a reductive Lie algebra over ℂ and let b be a reductive subalgebra of a. The first result gives the formula for multiplicity with which a finite dimensional irreducible representation of b appears in a given finite dimensional irreducible representation of a in a general situation. This generalizes a known theorem due to Kostant in a special case. (2) LetG be a connected real semisimple Lie group andK a maximal compact subgroup ofG. The second result is a formula for multiplicity with which an irreducible representation ofK occurs in a generalized representation ofG arising not necessarily from fundamental Cartan subgroup ofG. This generalizes a result due to Enright and Wallach in a fundamental case.

    • Author Affiliations

       

      M S Bakre1

      1. Department of Mathematics, University of Bombay, Bombay - 400 098, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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