A Dolbeault-Dirac Spectral Triple for the B2-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 B2-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.

Keywords

• Noncommutative differential geometry
• quantum groups
• quantum flag manifolds
• spectral triples
• differential calcul