Representation theoretic harmonic spinors for coherent families

Mehdi, S. ; Parthasarathy, R. (2010) Representation theoretic harmonic spinors for coherent families Indian Journal of Pure and Applied Mathematics, 41 (1). pp. 133-144. ISSN 0019-5588

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Coherent continuation π2 of a representation π1 of a semisimple Lie algebra arises by tensoring π1 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.

Item Type:Article
Source:Copyright of this article belongs to Indian National Science Academy.
Keywords:Semisimple Lie group; Enright-Varadarajan module; Dirac Cohomology; Zuckerman Translation Functor; Coherent Family; Harmonic Spinor
ID Code:33914
Deposited On:21 Mar 2011 10:06
Last Modified:17 May 2016 16:48

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