A Clifford Algebraic Framework for $$\mathfrak{sp}(m)$$-Invariant Differential Operators |
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Authors: | David Eelbode |
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Institution: | (1) Dept. of Mathematical Analysis Clifford Research Group, Ghent University, Galglaan 2, 9000 Ghent, Belgium |
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Abstract: | We introduce a framework for studying differential operators which are invariant with respect to the real (complex) symplectic
Lie algebra
(
), associated to a quaternionic structure on a vector space
. To do so, these algebras are realized within the orthogonal Lie algebra
. This leads in a natural way to a refinement of the recently introduced notion of complex Hermitean Clifford analysis, in
which four variations of the classical Dirac operator play a dominant role.
David Eelbode: Postdoctoral fellow supported by the F.W.O. Vlaanderen (Belgium). |
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Keywords: | " target="_blank"> Quaternionic geometry invariant operators |
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