Speaker
Elmar Wagner
Description
The Berstein-Gelfand-Gelfand resolution for irreducible quantum flag manifolds gives an algebraic description of the Dolbeault complex of (anti-)holomorphic k-forms by actions of quantum tangent space. Requiring equivariance and compatibility with the real form of the quantum enveloping algebra, there is an essentially unique hermitian metric on the (0,k)-forms given by the Haar state. Using equivariance, spectral computations can be reduced to determining the eigenvalues of the Laplace operator on 1-dimensional highest weight spaces.
