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SUMMARY:Degenerate Representations of GL_n over a p-adic field - Johannes 
 Girsch (University of Durham)
DTSTART:20260317T143000Z
DTEND:20260317T153000Z
UID:TALK242821@talks.cam.ac.uk
CONTACT:Dmitri Whitmore
DESCRIPTION:Smooth generic representations of $GL_n$ over a $p$-adic field
  $F$\, i.e. representations admitting a nondegenerate Whittaker model\, ar
 e an important class of representations\, for example in the setting of Ra
 nkin-Selberg integrals. However\, in recent years there has been an increa
 sed interest in non-generic representations and their degenerate Whittaker
  models. By the theory of Bernstein-Zelevinsky derivatives we can associat
 e to each smooth irreducible representation of $GL_n(F)$ an integer partit
 ion of $n$\, which encodes the "degeneracy" of the representation. By usin
 g these "highest derivative partitions" we can define a stratification of 
 the category of smooth complex representations and prove the surprising fa
 ct that all of the strata categories are equivalent to module categories o
 ver commutative rings. This is joint work with David Helm.
LOCATION:MR13
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