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The Symplectic Fueter–Sce Theorem

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Abstract

In this paper we present a symplectic analogue of the Fueter theorem. This allows the construction of special (polynomial) solutions for the symplectic Dirac operator \(D_s\), which is defined as the first-order \(\mathfrak {sp}(2n)\)-invariant differential operator acting on functions on \(\mathbb {R}^{2n}\) taking values in the metaplectic spinor representation.

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Authors and Affiliations

  1. Department of Mathematics, University of Antwerp, Middelheim Campus, Building G, Middelheimlaan 1, 2020, Antwerp, Belgium

    David Eelbode, Sonja Hohloch & Guner Muarem

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  1. David Eelbode
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  2. Sonja Hohloch
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  3. Guner Muarem
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Correspondence to Guner Muarem.

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Communicated by Hendrik De Bie.

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Eelbode, D., Hohloch, S. & Muarem, G. The Symplectic Fueter–Sce Theorem. Adv. Appl. Clifford Algebras 30, 49 (2020). https://doi.org/10.1007/s00006-020-01077-5

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  • DOI: https://doi.org/10.1007/s00006-020-01077-5

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