An Exceptional Symmetry Algebra for the 3D Dirac–Dunkl Operator

2020/01/01 by Alexis Langlois-Rémillard, Roy Oste · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Computer science #Dirac (video compression format) #Dirac algebra #Dirac equation #Dirac operator #Geometry #Group (periodic table) #Homogeneous space #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Operator (biology) #Operator algebra #Physics #Pure mathematics #Quantum mechanics #Reflection (computer programming) #Reflection group #Space (punctuation) #Symmetry (geometry) #Symmetry group #Weyl group #math-ph #math.MP #math.RT

paper · pdf · doi:10.1007/978-981-15-7775-8_30

7 pages; to be published in Springer Proceedings in Mathematics & Statistics

openalex publication_date 2020/01/01 · arxiv created 2020/09/29 · arxiv updated 2021/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We initiate the study of an algebra of symmetries for the 3D Dirac-Dunkl operator associated with the Weyl group of the exceptional root system G₂. For this symmetry algebra, we give both an abstract definition and an explicit realisation. We then construct ladder operators, using an intermediate result we prove for the Dirac-Dunkl symmetry algebra associated with arbitrary finite reflection group acting on a three-dimensional space.

Citations

• Lecture notes on Cherednik algebras

Cited by

• Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl–Dirac operator