Journal article
Symplectic Dirac operators for Lie algebras and graded Hecke algebras
- Abstract:
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
-
-
(Preview, Accepted manuscript, pdf, 445.4KB, Terms of use)
-
- Publisher copy:
- 10.1007/s00031-022-09762-4
Authors
+ Engineering and Physical Sciences Research Council
More from this funder
- Grant:
- EP/V046713/1
- EP/N033922/1
- Publisher:
- Springer
- Journal:
- Transformation Groups More from this journal
- Volume:
- 28
- Issue:
- 4
- Pages:
- 1447–1475
- Publication date:
- 2022-08-20
- Acceptance date:
- 2022-02-14
- DOI:
- EISSN:
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1531-586X
- ISSN:
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1083-4362
- Language:
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English
- Pubs id:
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1239722
- Local pid:
-
pubs:1239722
- Deposit date:
-
2022-02-14
Terms of use
- Copyright holder:
- Springer Science+Business Media New York
- Copyright date:
- 2022
- Rights statement:
- ©Springer Science+Business Media New York (2022).
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Springer at: https://doi.org/10.1007/s00031-022-09762-4
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