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arXiv · 2109.09885

A Dolbeault-Dirac Spectral Triple for the $B_2$-Irreducible Quantum Flag Manifold

Fredy Díaz García·Réamonn Ó Buachalla·Elmar Wagner
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Abstract

The quantum version of the Bernstein-Gelfand-Gelfand resolution is used to construct a Dolbeault-Dirac operator on the anti-holomorphic forms of the Heckenberger-Kolb calculus for the $B_2$-irreducible quantum flag manifold. The spectrum and the multiplicities of the eigenvalues of the Dolbeault-Dirac operator are computed. It is shown that this construction yields an equivariant, even, $0^+$-summable spectral triple.

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Fredy Díaz García, Réamonn Ó Buachalla, Elmar Wagner. 2021-09-20. A Dolbeault-Dirac Spectral Triple for the $B_2$-Irreducible Quantum Flag Manifold. https://arxiv.org/abs/2109.09885

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