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SUMMARY:Pavel Etingof (MIT)
DTSTART:20200703T201000Z
DTEND:20200703T210000Z
DTSTAMP:20260415T050923Z
UID:T-Rep/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/T-Rep/2/">Ne
 w incompressible symmetric tensor categories in positive characteristic</a
 >\nby Pavel Etingof (MIT) as part of T-Rep: A midsummer night's session on
  representation theory and tensor categories\n\n\nAbstract\nLet k be an al
 gebraically closed field of characteristic p>0. The category of tilting mo
 dules for SL2(k) has a tensor ideal In generated by the n-th Steinberg mod
 ule. I will explain that the quotient of the tilting category by In admits
  an abelian envelope\, a finite symmetric tensor category Verpn\, which is
  not semisimple for n>1. This is a reduction to characteristic p of the se
 misimplification of the category of tilting modules for the quantum group 
 at a root of unity of order pn. These categories are incompressible\, i.e.
  do not admit fiber functors to smaller categories. For p=1\, these catego
 ries were defined by S. Gelfand and D. Kazhdan and by G. Georgiev and O. M
 athieu in early 1990s\, but for n>1 they are new. I will describe these ca
 tegories in detail and explain a conjectural formulation of Deligne's theo
 rem in characteristic p in which they appear. This is joint work with D. B
 enson and V. Ostrik.\n
LOCATION:https://researchseminars.org/talk/T-Rep/2/
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