The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator

DOI10.1016/j.geomphys.2013.09.005zbMath1279.30051arXiv1002.1053OpenAlexW1992944552MaRDI QIDQ391161

Hendrik De Bie, Petr Somberg, Vladimír Souček

Publication date: 10 January 2014

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

Full work available at URL: https://arxiv.org/abs/1002.1053

zbMATH Keywords

Fischer decompositionHowe dualitysymplectic Dirac operatorsymplectic monogenics

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Functions of hypercomplex variables and generalized variables (30G35)

Related Items

Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator ⋮ The orthogonal branching problem for symplectic monogenics ⋮ Fischer decomposition in generalized fractional ternary Clifford analysis ⋮ The symplectic Fueter-Sce theorem ⋮ Differential invariants on symplectic spinors in contact projective geometry ⋮ Fischer Decomposition and Cauchy–Kovalevskaya Extension in Fractional Clifford Analysis: The Riemann–Liouville Case ⋮ Fischer Decomposition in Generalized Fractional Clifford Analysis ⋮ The harmonic transvector algebra in two vector variables ⋮ Conformal symmetries of the super Dirac operator

Cites Work

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• Conformal symmetries of the super Dirac operator
• The Howe duality for the Dunkl version of the Dirac operator
• Fourier transform and related integral transforms in superspace
• The Howe dual pair in Hermitean Clifford analysis
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Correct rules for Clifford calculus on superspace
• Introduction to symplectic Dirac operators
• Transcending Classical Invariant Theory
• Spherical harmonics and integration in superspace: II
• Remarks on Classical Invariant Theory
• On modules of bounded multiplicities for the symplectic algebras
• A Hodge type decomposition for spinor valued forms
• Spherical harmonics and integration in superspace

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