Seminar Algebra and Geometry: Markus Hunziker (Baylor University, Texas)

Classical Invariant Theory and Category O

In this talk, I will show how to solve several famous problems (old and new) from classical invariant theory by using the structure of certain categories of highest weight modules. For example, the structure of a category of highest weight modules for the symplectic Liealgebra sp_2n(C) will be used to compute minimal free resolutions (syzygies) and Hilbertseries of the modules of covariants for the action of the orthogonal group O_k(C) on C_k⊕···⊕C_k( n-copies). This in turn leads to a simple characterization of the Cohen–Macaulaymodules of covariants.

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