Symplectic Dirac operators for Lie algebras and graded Hecke algebras

2020/03/25 by Dan Ciubotaru, Ciubotaru, Dan, Marcelo De Martino +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2003.11279

openalex publication_date 2020/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We 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 \mathbb Z/2-graded quadratic Lie algebras \mathfrak g=\mathfrak k+\mathfrak p and of graded affine Hecke algebras \mathbb H.

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