Geodesic
The cubic Dirac operator on compact quotients of the oscillator group
Documenta mathematica, Tome 29 (2024) no. 4, pp. 985-1016

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We study Kostant’s cubic Dirac operator D1/3 on locally symmetric Lorentzian manifolds of the form Γ\Osc1​, where Osc1​ is the four-dimensional oscillator group and Γ⊂Osc1​ is a cocompact lattice. These quotients are the only four-dimensional, compact Lorentzian G-homoge­neous spaces for a solvable but non-abelian Lie group G. We determine the spectrum of D1/3. We also give an explicit decomposition of the regular representation of Osc1​ on L2-sections of the spinor bundle into irreducible subrepresentations and we determine the eigenspaces of D1/3.
DOI : 10.4171/dm/967
Classification : 53C50, 35Q41, 58J50, 22E27
Mots-clés : Lorentzian manifold, cubic Dirac operator, locally symmetric space 
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Ines Kath; Margarita Kraus. The cubic Dirac operator on compact quotients of the oscillator group. Documenta mathematica, Tome 29 (2024) no. 4, pp. 985-1016. doi: 10.4171/dm/967

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