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Noncommutative Geometry and Topology Seminar

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

Speaker’s name: 
Fredy Díaz
Speaker’s affiliation: 
Charles University


Blue Room, Institute of Mathematics CAS, Zitna  25, Praha 1
Tuesday, 5. October 2021 - 16:00 to 17:30
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.