Representation theoretic harmonic spinors for coherent families

S. Mehdi () and R. Parthasarathy ()
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S. Mehdi: Université de Metz
R. Parthasarathy: Tata Institute of Fundamental Research

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 1, 133-144

Abstract: 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.

Keywords: Semisimple lie group; Enright-Varadarajan module; Dirac cohomology; Zuckerman translation functor; Coherent family; harmonic spinor (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0011-3

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