Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl–Dirac operator
| Autor: | Roy Oste, Joris Van der Jeugt, Hendrik De Bie, Alexis Langlois-Rémillard |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Polynomial
Rank (linear algebra) Mathematics::Classical Analysis and ODEs FOS: Physical sciences Dirac operator symbols.namesake Mathematics::Quantum Algebra FOS: Mathematics Representation Theory (math.RT) Mathematics::Representation Theory Mathematical Physics Dunkl operator Mathematics Algebra and Number Theory Unitarity Operator (physics) Clifford algebra Finite-dimensional representations Mathematical Physics (math-ph) Dihedral root systems Total angular Algebra Mathematics and Statistics Tensor product Symmetry algebra operator symbols Dunkl-Dirac equation Mathematics - Representation Theory |
| Zdroj: | JOURNAL OF ALGEBRA |
| ISSN: | 0021-8693 1090-266X |
| DOI: | 10.1016/j.jalgebra.2021.09.025 |
| Popis: | 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. Comment: v3 40p. Final version accepted in J. Algebra. See v2 for proof of Thm 4.1 |
| Databáze: | OpenAIRE |
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