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Cluster Ensembles and the Chamber Ansatz

Harold Williams
(UC Berkeley)
Seminar
Torsdag, 20 september, 2012, at 15:00-16:00, in Aud. D4 (1531-219)
Abstrakt:
Cluster ensembles axiomatize certain structures appearing in higher Teichmuller theory, and extend the notion of a cluster algebra. The essential data is a canonical transformation between a collection of cluster variables and another type of coordinates, often called coefficient variables or X-coordinates. This same structure arises in a number of other contexts where cluster algebras are present, though often in a disguised form. We will explain a particular example of this coming from Lie theory, related in particular to loop groups and integrable systems. In fact, we will see that the notion of a cluster ensemble turns out in retrospect to provide a useful point of view on the Chamber Ansatz, a key formula in the theory of total positivity in simple algebraic groups
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen