Some exotic tensor categories in prime characteristic.

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• David Benson (Aberdeen)
• Wednesday 19 February 2020, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Christopher Brookes.

This talk is about joint work with Pavel Etingof and Victor Ostrik. A theorem of Deligne says that in characteristic zero, any symmetric tensor category “of moderate growth” admits a tensor functor to vector spaces or to super (i.e., Z/2-graded) vector spaces. In prime characteristic, this is not true, but one may ask whether there is a good list of “incompressible” symmetric tensor categories to which they they do all map. We construct an infinite ascending chain of finite symmetric tensor categories in characteristic p, all of which are incompressible. The constructions are based on the theory of tilting modules over the algebraic group SL(2). It is possible that this is the complete list, but we have not proved that.

This talk is part of the Algebra and Representation Theory Seminar series.

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