SYMPLECTIC DIRAC OPERATORS FOR LIE ALGEBRAS AND GRADED HECKE ALGEBRAS

被引：0
|
作者：
Ciubotaru, D. [1 ]
De Martino, M. [1 ]
Meyer, P. [1 ]
机构：
[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England
来源：
TRANSFORMATION GROUPS | 2023年 / 28卷 / 04期
基金：
英国工程与自然科学研究理事会;
关键词：
REPRESENTATIONS;
D O I：
10.1007/s00031-022-09762-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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 DOUBLE-STRUCK CAPITAL 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：29
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