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
mehdi@math.jussieu.fr
Rajagopalan Parthasarathy
School of Mathematics, T. I. F. R., Homi Bhabha Road, Mumbai 400005, India
sarathy@math.tifr.res.in
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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