Symplectic Dirac operators for Lie algebras and graded Hecke algebras
The aim of this paper is to define a pair of symplectic Dirac operators (D+, D–) in an algebraic setting motivated by the analogy with the algebraic orthogonal Dirac operators in representation theory. We work in the settings of ℤ/2-graded quadratic Lie algebras 𝔤 = 𝔨 + 𝔭 and of graded affine Hecke...
| Asıl Yazarlar: | , , |
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| Materyal Türü: | Journal article |
| Dil: | English |
| Baskı/Yayın Bilgisi: |
Springer
2022
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| _version_ | 1826312297432219648 |
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| author | Ciubotaru, D De Martino, M Meyer, P |
| author_facet | Ciubotaru, D De Martino, M Meyer, P |
| author_sort | Ciubotaru, D |
| collection | OXFORD |
| description | The aim of this paper is to define a pair of symplectic Dirac operators (D+, D–) in an algebraic setting motivated by the analogy with the algebraic orthogonal Dirac operators in representation theory. We work in the settings of ℤ/2-graded quadratic Lie algebras 𝔤 = 𝔨 + 𝔭 and of graded affine Hecke algebras ℍ. In these contexts, we show analogues of the Parthasarathy’s formula for [D+, D–] and certain generalisations of the Casimir inequality. |
| first_indexed | 2024-03-07T08:26:55Z |
| format | Journal article |
| id | oxford-uuid:e6f57bb7-cb01-45a2-a0d6-213dd5bd352e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:26:55Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:e6f57bb7-cb01-45a2-a0d6-213dd5bd352e2024-02-15T08:44:53ZSymplectic Dirac operators for Lie algebras and graded Hecke algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e6f57bb7-cb01-45a2-a0d6-213dd5bd352eEnglishSymplectic ElementsSpringer2022Ciubotaru, DDe Martino, MMeyer, PThe aim of this paper is to define a pair of symplectic Dirac operators (D+, D–) in an algebraic setting motivated by the analogy with the algebraic orthogonal Dirac operators in representation theory. We work in the settings of ℤ/2-graded quadratic Lie algebras 𝔤 = 𝔨 + 𝔭 and of graded affine Hecke algebras ℍ. In these contexts, we show analogues of the Parthasarathy’s formula for [D+, D–] and certain generalisations of the Casimir inequality. |
| spellingShingle | Ciubotaru, D De Martino, M Meyer, P Symplectic Dirac operators for Lie algebras and graded Hecke algebras |
| title | Symplectic Dirac operators for Lie algebras and graded Hecke algebras |
| title_full | Symplectic Dirac operators for Lie algebras and graded Hecke algebras |
| title_fullStr | Symplectic Dirac operators for Lie algebras and graded Hecke algebras |
| title_full_unstemmed | Symplectic Dirac operators for Lie algebras and graded Hecke algebras |
| title_short | Symplectic Dirac operators for Lie algebras and graded Hecke algebras |
| title_sort | symplectic dirac operators for lie algebras and graded hecke algebras |
| work_keys_str_mv | AT ciubotarud symplecticdiracoperatorsforliealgebrasandgradedheckealgebras AT demartinom symplecticdiracoperatorsforliealgebrasandgradedheckealgebras AT meyerp symplecticdiracoperatorsforliealgebrasandgradedheckealgebras |