Spinor-valued and Clifford algebra-valued harmonic polynomials

DOI10.1016/S0393-0440(00)00045-0zbMath0972.43005MaRDI QIDQ5932172

Yasushi Homma

Publication date: 2 November 2001

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

\( \text{Spin} (n)\)-modulesClifford algebra valued polynomialsinvariant operators

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Elliptic equations on manifolds, general theory (58J05) Harmonic analysis and spherical functions (43A90)

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The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces ⋮ On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain ⋮ Spherical harmonic polynomials for higher bundles ⋮ On polynomial solutions of generalized Moisil-Théodoresco systems and Hodge-de Rham systems ⋮ On the spectrum of spherical Dirac-type operators ⋮ Conformally equivariant quantization for spinning particles ⋮ The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces

Cites Work

• The Dirac operator on homogeneous spaces and its spectrum on 3- dimensional lens spaces
• Spectra and eigenforms of the Laplacian on \(S^n\) and \(P^n(C)\)
• Stein-Weiss operators and ellipticity
• The Dirac operator on space forms of positive curvature
• Clifford modules
• Harmonic analysis of the de Rham complex on the sphere.
• A representation of \(\text{Spin}(4)\) on the eigenspinors of the Dirac operator on \(S^3\)
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