Variations on a theme of J.-P. Serre: Complete reducibility in groups, representations, buildings and geometric invariant theory

Abstract: When studying modules or other algebraic objects, it is common to try and break things up and study the simple pieces. Complete reducibility asks the question: Under what conditions do these simple objects fully describe the object we started with? In representation theory this becomes: Under what condition is every module a direct sum of its irreducible factors? This question, which a priori has nothing to do with geometry, topology or combinatorics, turns out to have deep connections with all these other areas. In this talk we will look at these connections, and we will see how fundamental representation-theoretic results have analogues and generalisations in other areas of pure mathematics.

algebraic geometrygroup theoryrepresentation theory

Audience: researchers in the discipline

MESS (Mathematics Essex Seminar Series)

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