Dirac Operators for the Dunkl Angular Momentum Algebra

Kieran Calvert, Marcelo De Martino

Research output: Contribution to journalArticlepeer-review


We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements of the group algebra of the Pin cover of the Weyl group inherent to the rational Cherednik algebra. We prove an analogue of Vogan’s conjecture for this family of operators and use this to show that the Dirac cohomology, when non-zero, determines the central character of representations of the angular momentum algebra. Furthermore, interpreting this algebra in the framework of (deformed) Howe dualities, we show that the natural Dirac element we define yields, up to scalars, a square root of the angular part of the Calogero–Moser Hamiltonian.

Original languageEnglish
Article number040
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Publication statusPublished - 2022


  • Calogero–Moser angular momentum
  • Dirac operators
  • rational Cherednik algebras


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