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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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Publisher copy:
10.1007/s00031-022-09762-4

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Somerville College
Role:
Author
ORCID:
0000-0002-7921-9691
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author


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:
1531-586X
ISSN:
1083-4362


Language:
English
Pubs id:
1239722
Local pid:
pubs:1239722
Deposit date:
2022-02-14

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