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Representation theoretic harmonic spinors for coherent families

Author

Listed:
  • S. Mehdi

    (Université de Metz)

  • R. Parthasarathy

    (Tata Institute of Fundamental Research)

Abstract

Coherent continuation π 2 of a representation π 1 of a semisimple Lie algebra arises by tensoring π 1 with a finite dimensional representation F and projecting it to the eigenspace of a particular infinitesimal character. Some relations exist between the spaces of harmonic spinors (involving Kostant’s cubic Dirac operator and the usual Dirac operator) with coefficients in the three modules. For the usual Dirac operator we illustrate with the example of cohomological representations by using their construction as generalized Enright-Varadarajan modules. In [9] we considered only discrete series, which arises as generalized Enright-Varadarajan modules in the particular case when the parabolic subalgebra is a Borel subalgebra.

Suggested Citation

  • S. Mehdi & R. Parthasarathy, 2010. "Representation theoretic harmonic spinors for coherent families," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(1), pages 133-144, February.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:1:d:10.1007_s13226-010-0011-3
    DOI: 10.1007/s13226-010-0011-3
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