Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations
Let be a Clifford module for the complexified Clifford algebra ℂℓ(ℝⁿ), ′ its dual, ρ and ρ′ be the corresponding representations of the spin group Spin(). The group G=Spin(1, +1) is a (twofold) covering of the conformal group of ℝⁿ. For λ, μ ∈ ℂ, let πρ,λ (resp. πρ′,μ) be the spinorial representati...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211300 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations. Jean-Louis Clerc and Khalid Koufany. SIGMA 17 (2021), 049, 23 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let be a Clifford module for the complexified Clifford algebra ℂℓ(ℝⁿ), ′ its dual, ρ and ρ′ be the corresponding representations of the spin group Spin(). The group G=Spin(1, +1) is a (twofold) covering of the conformal group of ℝⁿ. For λ, μ ∈ ℂ, let πρ,λ (resp. πρ′,μ) be the spinorial representation of realized on a (subspace of) C∞(ℝⁿ, ) (resp. C∞(ℝⁿ, ′)). For 0 ≤ ≤ and ∈ ℕ, we construct a symmetry-breaking differential operator ⁽ᵐ⁾k;λ,μ from C∞(ℝⁿ×ℝⁿ, ⊗ ′) into C∞(ℝⁿ, Λ*ₖ(ℝⁿ)⊗ ℂ) which intertwines the representations πρ,λ⊗πρ′,μ and πτ∗ₖ,λ₊μ₊₂ₘ, where τ*ₖ is the representation of Spin() on the space Λ*ₖ(ℝⁿ)⊗ ℂ of complex-valued alternating -forms on ℝⁿ.
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| ISSN: | 1815-0659 |