Abstract
The authors of (Stein, Weiss) introduced the general method of construction of first order differential operators based on covariant derivatives composed with projections onto irreducible components of the target space. Following this general construction, we introduce, inside parabolic geometry (parabolic invariant theory), the symplectic Dirac operator first defined via analytical methods by K.Haberman. The role of the spinor bundle in orthogonal case is played here (in the symplectic case) by Segal-Shale-Weil representation. This representation is infinite-dimensional, so the Harish-Chandra category of K = U(n)-finite modules must be introduced.
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© 2001 Springer Science+Business Media Dordrecht
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Kadlčáková, L. (2001). Contact Symplectic Geometry in Parabolic Invariant Theory and Symplectic Dirac Operator. In: Brackx, F., Chisholm, J.S.R., Souček, V. (eds) Clifford Analysis and Its Applications. NATO Science Series, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0862-4_10
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DOI: https://doi.org/10.1007/978-94-010-0862-4_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7045-1
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