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SUMMARY:Bernoulli Lecture - Representation theory of symmetric groups and 
 categorification
DTSTART:20161215T171500
DTEND:20161215T181500
DTSTAMP:20260920T164834Z
UID:942b13040cee52acfa18756e2f08cb9c560f1cca0bd3858c174a5279
CATEGORIES:Conferences - Seminars
DESCRIPTION:Alexander Kleshchev (University of Oregon)\nWe review recent (
 ~20 years) advances in representation theory of symmetric groups with the 
 emphasis on categorification techniques.\n\nBranching rules describe restr
 ictions of irreducible representations of a symmetric group to a smaller s
 ymmetric group. Studying branching rules leads one to a categorification i
 dea: restriction and induction functors yield a categorical action of cert
 ain Lie algebras on representation categories of symmetric groups. The cor
 responding action of the Weyl group lifts to a derived equivalence between
  the blocks of the symmetric groups (Chuang-Rouquier). Connections with Kh
 ovanov-Lauda-Rouquier algebras tie the categorical actions to quantum grou
 ps.\n\nIn the very end\, we present a joint result with Anton Evseev\, whi
 ch describes every block of a symmetric group up to derived equivalence as
  a certain Turner double algebra. This description was conjectured by Will
  Turner. Turner doubles are Schur-algebra-like 'local' objects\, which rep
 lace wreath products of Brauer tree algebras in the context of the Broué 
 abelian defect group conjecture for blocks of symmetric groups with non-ab
 elian defect groups.\n\nMost of the ideas presented in the talk hold much 
 more generally\, but we stick mostly to symmetric groups to make presentat
 ion non-technical.
LOCATION:BI A0 448 https://plan.epfl.ch/?room==BI%20A0%20448
STATUS:CONFIRMED
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