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Dirac Operators for the Dunkl Angular Momentum Algebra
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Dirac operators, Calogero–Moser angular momentum, rational Cherednik algebras. 
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     author = {Kieran Calvert and Marcelo De Martino},
     title = {Dirac {Operators} for the {Dunkl} {Angular} {Momentum} {Algebra}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a39/}
}
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Kieran Calvert; Marcelo De Martino. Dirac Operators for the Dunkl Angular Momentum Algebra. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a39/

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