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SUMMARY:Vera Serganova (University of California\, Berkeley)
DTSTART:20200703T183000Z
DTEND:20200703T192000Z
DTSTAMP:20260415T015126Z
UID:T-Rep/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/T-Rep/1/">Th
 e Jacobson-Morozov theorem for Lie superalgebras via semisimplification fu
 nctor for tensor categories</a>\nby Vera Serganova (University of Californ
 ia\, Berkeley) as part of T-Rep: A midsummer night's session on representa
 tion theory and tensor categories\n\n\nAbstract\nThe celebrated Jacobson-M
 orozov theorem claims that every nilpotent element of a semisimple Lie alg
 ebra g can be embedded into an sl(2)-triple inside g. Let g be a Lie super
 algebra with reductive even part and x be an odd element of g with non-zer
 o nilpotent [x\,x]. We give necessary and sufficient condition when x can 
 be embedded in osp(1|2) inside g. The proof follows the approach of Etingo
 f and Ostrik and involves semisimplification functor for tensor categories
 . Next\, we will show that for every odd x in g we can construct a symmetr
 ic monoidal functor between categories of representations of certain super
 algebras. We discuss some properties of these functors and applications of
  them to representation theory of superalgebras with reductive even part. 
 We also discuss possible generalization of reductive envelope of an algebr
 aic group to the case of a supergroup. (Joint work with Inna Entova-Aizenb
 ud).\n
LOCATION:https://researchseminars.org/talk/T-Rep/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20200703T201000Z
DTEND:20200703T210000Z
DTSTAMP:20260415T015126Z
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/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Coulembier (University of Sydney)
DTSTART:20200703T211000Z
DTEND:20200703T220000Z
DTSTAMP:20260415T015126Z
UID:T-Rep/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/T-Rep/3/">Mo
 noidal abelian envelopes</a>\nby Kevin Coulembier (University of Sydney) a
 s part of T-Rep: A midsummer night's session on representation theory and 
 tensor categories\n\n\nAbstract\nThe notion of an abelian envelope of a k-
 linear rigid monoidal category emerged rather recently from the constructi
 ons by Entova-Hinich-Serganova and Comes-Ostrik of universal tensor catego
 ries. They subsequently reappeared in a construction by Benson-Etingof of 
 an intriguing family of incompressible tensor categories in characteristic
  2. All of this clearly demanded a thorough exploration of this concept of
  abelian envelopes. In this talk I will report on recent progress on the m
 atter due to a number of authors.\n
LOCATION:https://researchseminars.org/talk/T-Rep/3/
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