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Algebra Seminar
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Gus Lehrer
University of Sydney

The topology of the variety of regular semisimple elements of a complex Lie algebra

Friday 22nd August, 12:05-12:55pm, Carslaw 373.

The regular semisimple elements form an open dense subvariety g_{rs} of a complex Lie algebra (or group); for example in type A, it is the space of matrices with distinct eigenvalues. This variety is important in several contexts, including its role in the "Grothendieck-Springer resolution", where one interpolates between it and the nilpotent cone. I shall describe how the topology of g_{rs} may be analysed in the classical cases by establishing connections between it, configuration spaces and iterated loop spaces. This is joint work with Graeme Segal.