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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | 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 |
| Цитувати: | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations. Jean-Louis Clerc and Khalid Koufany. SIGMA 17 (2021), 049, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862752381013327872 |
|---|---|
| author | Clerc, Jean-Louis Koufany, Khalid |
| author_facet | Clerc, Jean-Louis Koufany, Khalid |
| citation_txt | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations. Jean-Louis Clerc and Khalid Koufany. SIGMA 17 (2021), 049, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-04-17T20:51:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211300 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T20:51:43Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Clerc, Jean-Louis Koufany, Khalid 2025-12-29T11:05:54Z 2021 Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations. Jean-Louis Clerc and Khalid Koufany. SIGMA 17 (2021), 049, 23 pages 1815-0659 2020 Mathematics Subject Classification: 43A85; 58J70; 33J45 arXiv:2012.09625 https://nasplib.isofts.kiev.ua/handle/123456789/211300 https://doi.org/10.3842/SIGMA.2021.049 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. At the very beginning of the present work, the first author benefited from a discussion with Bent Ørsted during a visit to Aarhus University and wishes to thank him and his institution for the invitation. The authors are very grateful to the anonymous referees for their expert comments and suggestions, which helped to improve the initial version of this article. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations Article published earlier |
| spellingShingle | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations Clerc, Jean-Louis Koufany, Khalid |
| title | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations |
| title_full | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations |
| title_fullStr | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations |
| title_full_unstemmed | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations |
| title_short | Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations |
| title_sort | symmetry breaking differential operators for tensor products of spinorial representations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211300 |
| work_keys_str_mv | AT clercjeanlouis symmetrybreakingdifferentialoperatorsfortensorproductsofspinorialrepresentations AT koufanykhalid symmetrybreakingdifferentialoperatorsfortensorproductsofspinorialrepresentations |