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Cluster structures in rings of SL_3 invariants October 09, 2012 (02:00 PM PDT - 03:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Sergey Fomin (University of Michigan)
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The rings of polynomial SL(V)-invariants of configurations of vectors and linear forms in a k-dimensional complex vector space V have been explicitly described by Hermann Weyl in the 1930s. Each such ring conjecturally carries a natural cluster algebra structure (typically, many of them) whose cluster variables include Weyl's generators. In joint work with Pavlo Pylyavskyy, we describe and explore these cluster structures in the case k=3. We employ the machinery of tensor diagrams, and make a connection to the web bases introduced by G. Kuperberg.

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