SYMPLECTIC DIRAC OPERATORS FOR LIE ALGEBRAS AND GRADED HECKE ALGEBRAS

被引：0
|
作者：
D. CIUBOTARU
M. DE MARTINO
P. MEYER
机构：
[1] University of Oxford,Mathematical Institute
来源：
Transformation Groups | 2023年 / 28卷
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摘要：
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.
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页码：1447 / 1475
页数：28
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