Higher Spin Dirac Operators Between Spaces of Simplicial Monogenics in Two Vector Variables |
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| Authors: | F Brackx D Eelbode L Van de Voorde |
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| Institution: | 1.Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering,Ghent University,Ghent,Belgium;2.Department of Mathematics and Computer Science,University of Antwerp,Antwerp,Belgium |
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| Abstract: | The higher spin Dirac operator \(\mathcal{Q}_{k,l}\) acting on functions taking values in an irreducible representation space for \(\mathfrak{so}(m)\) with highest weight \((k+\frac{1}{2},l+\frac{1}{2},\frac{1}{2},\ldots,\frac{1}{2})\), with k, l?∈?\(\mathbb{N}\) and \(k\geqslant l\), is constructed. The structure of the kernel space containing homogeneous polynomial solutions is then also studied. |
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