Noncommutative Geometry and Topology Seminar

A Dolbeault-Dirac spectral triple for the B2-irreducible quantum flag manifold.

In this talk we present the construction of the Dolbeault–Dirac operator associated to the B2-quantum flag manifold. The main ingredients are the quantum version of the Bernstein–Gelfand–Gelfand resolution for irreducible flag manifolds and the representation theory of the quantum group U_q(\mathfrak{so}(5)). We will show that a U_q(\mathfrak{so}(5))-co-equivariant, 0+-summable, even spectral triple can be constructed as well as we give a complete description of the spectrum of the Dirac operator.