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Harmonic Spinors on Hyperbolic Space

Published online by Cambridge University Press:  20 November 2018

Pierre-Yves Gaillard
Pierre-Yves Gaillard*
Affiliation:
Département de mathématiques Université du Québec CP 8888, suce. A Montréal, Québec H3C 3P8
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Abstract

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The purpose for this short note is to describe the space of harmonic spinors on hyperbolic n-space Hn. This is a natural continuation of the study of harmonic functions on Hn in [Minemura] and [Helgason]—these results were generalized in the form of Helgason's conjecture, proved in [KKMOOT],—and of [Gaillard 1, 2], where harmonic forms on Hn were considered. The connection between invariant differential equations on a Riemannian semisimple symmetric space G/K and homological aspects of the representation theory of G, as exemplified in (8) below, does not seem to have been previously mentioned. This note is divided into three main parts respectively dedicated to the statement of the results, some reminders, and the proofs. I thank the referee for having suggested various improvements.

Keywords

55R2558G25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 3 , 01 September 1993 , pp. 257 - 262
Copyright
Copyright © Canadian Mathematical Society 1993

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