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Journal of Lie Theory 18 (2008), No. 1, 033--044
Copyright Heldermann Verlag 2008

A Product for Harmonic Spinors on Reductive Homogeneous Spaces

Salah Mehdi
UFR SEGMI, Université Paris 10, 200 Av. de la République, 92001 Nanterre, France

Rajagopalan Parthasarathy
School of Mathematics, T. I. F. R., Homi Bhabha Road, Mumbai 400005, India

We define a product for harmonic spinors on reductive homogeneous spaces. We give also some examples where harmonic spinors with coefficients in a module are expressed as a linear combination of products of harmonic spinors with coefficients in two other modules. One such example involves discrete series representations.

Keywords: Reductive Lie group, Enright-Varadarajan module, Zuckerman translation functor, homogeneous space, harmonic spinor.

MSC: 22E47, 22F30; 43A85

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