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

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.