The orthogonal branching problem for symplectic monogenics

DOI10.1007/s00006-022-01215-1zbMath1495.17008arXiv2112.00421OpenAlexW3217352209MaRDI QIDQ2141074

Guner Muarem, David Eelbode

Publication date: 23 May 2022

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.00421

zbMATH Keywords

Dirac operatorrepresentation theorybranchingtransvector algebrassymplectic Clifford analysis

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Symplectic manifolds (general theory) (53D05) Clifford algebras, spinors (15A66) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47) Applications of Clifford algebras to physics, etc. (15A67)

Cites Work

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• The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator
• The harmonic transvector algebra in two vector variables
• Models for irreducible representations of Spin\((m)\)
• Symmetry breaking operators for real reductive groups of rank one
• Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator
• Introduction to symplectic Dirac operators
• Fischer decomposition for osp(4|2)-monogenics in quaternionic Clifford analysis
• Stable branching rules for classical symmetric pairs
• Symmetry, Representations, and Invariants
• EXTREMAL PROJECTORS AND GENERALIZED MICKELSSON ALGEBRAS OVER REDUCTIVE LIE ALGEBRAS
• Infinitesimal operators for representations of complex Lie groups and Clebsch-Gordan coefficients for compact groups
• Symplectic Dirac–Kähler fields
• Howe type duality for the metaplectic group acting on symplectic spinor valued forms
• Separation of Variables in the Semistable Range

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