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A Dolbeault-Dirac Spectral Triple for the $B_2$-Irreducible Quantum Flag Manifold (2109.09885v1)
Published 20 Sep 2021 in math.QA
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.