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CATEGORIES:Number Theory Seminar
SUMMARY:Degenerate Representations of GL_n over a p-adic f
 ield - Johannes Girsch (University of Durham)
DTSTART;TZID=Europe/London:20260317T143000
DTEND;TZID=Europe/London:20260317T153000
UID:TALK242821AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/242821
DESCRIPTION:Smooth generic representations of $GL_n$ over a $p
 $-adic field $F$\, i.e. representations admitting 
 a nondegenerate Whittaker model\, are an important
  class of representations\, for example in the set
 ting of Rankin-Selberg integrals. However\, in rec
 ent years there has been an increased interest in 
 non-generic representations and their degenerate W
 hittaker models. By the theory of Bernstein-Zelevi
 nsky derivatives we can associate to each smooth i
 rreducible representation of $GL_n(F)$ an integer 
 partition of $n$\, which encodes the "degeneracy" 
 of the representation. By using these "highest der
 ivative partitions" we can define a stratification
  of the category of smooth complex representations
  and prove the surprising fact that all of the str
 ata categories are equivalent to module categories
  over commutative rings. This is joint work with D
 avid Helm.
LOCATION:MR13
CONTACT:Dmitri Whitmore
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