2020/10/31 by Hendrik De Bie, Alexis Langlois-Rémillard, Roy Oste +2
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Clifford algebra #Dirac (video compression format) #Dirac algebra #Dirac equation #Dirac operator #Irreducible representation #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Unitarity #Yangian #math-ph #math.MP #math.RT
paper · pdf · doi:10.1016/j.jalgebra.2021.09.025
v3 40p. Final version accepted in J. Algebra. See v2 for proof of Thm 4.1
openalex publication_date 2021/10/28 · arxiv created 2021/11/03 · arxiv updated 2021/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Dunkl--Dirac operator is a deformation of the Dirac operator by means of Dunkl derivatives. We investigate the symmetry algebra generated by the elements supercommuting with the Dunkl--Dirac operator and its dual symbol. This symmetry algebra is realised inside the tensor product of a Clifford algebra and a rational Cherednik algebra associated with a reflection group or root system. For reducible root systems of rank three, we determine all the irreducible finite-dimensional representations and conditions for unitarity. Polynomial solutions of the Dunkl--Dirac equation are given as a realisation of one family of such irreducible unitary representations.