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On Some Generalization of B. Kostant’s Partition Function

  • Ichiro Amemiya
  • Nagayoshi Iwahori
  • Kazuhiko Koike
Part of the Progress in Mathematics book series (PM, volume 14)

Abstract

In this note we shall show some useful properties of the partition function given by B. Kostant [1] associated to complex semi-simple Lie algebras. Some of these properties are shown to be valid also for some generalized versions of Kostant’s partition function (see Theorem 1 below). As an application of these properties we give (Theorem 4) an explicit formula for the multiplicity of the zero-weight in a given irreducible representation of the simple Lie algebra of type (G2).

Keywords

Root System Partition Function Irreducible Representation Characteristic Content Zero Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    B. Kostant, “A formula for the multiplicity of a weight,” Trans. A.M.S., vol. 93, 53–73, 1959.Google Scholar
  2. [2]
    N. Bourbaki, Groupes et algèbre de Lie, Chap. 6, Hermann, Paris, 1968.Google Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Ichiro Amemiya
    • 1
  • Nagayoshi Iwahori
    • 1
  • Kazuhiko Koike
    • 1
  1. 1.University of TokyoBunkyoku, Tokyo 531Japan

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