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SUMMARY:Peiyi Cui (University of East Anglia)
DTSTART:20221102T160000Z
DTEND:20221102T170000Z
DTSTAMP:20260418T063717Z
UID:LNTS/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/77/">A 
 decomposition of the category of l-modular representations of SL_n(F).</a>
 \nby Peiyi Cui (University of East Anglia) as part of London number theory
  seminar\n\nLecture held in Huxley 139\, Imperial.\n\nAbstract\nLet F be a
  p-adic field\, and k an algebraically closed field of characteristic l di
 fferent from p. In this talk\, we will first give a category decomposition
  of Rep_k(SL_n(F))\, the category of smooth k-representations of SL_n(F)\,
  with respect to the GL_n(F)-equivalent supercuspidal classes of SL_n(F)\,
  which is not always a block decomposition in general. We then give a bloc
 k decomposition of the supercuspidal subcategory\, by introducing a partit
 ion on each GL_n(F)-equivalent supercuspidal class through type theory\, a
 nd we interpret this partition by the sense of l-blocks of finite groups. 
 We give an example where a block of Rep_k(SL_2(F)) is defined with respect
  to several SL_2(F)-equivalent supercuspidal classes\, which is different 
 from the case where l is zero. We end this talk by giving a prediction on 
 the block decomposition of Rep_k(A) for a general p-adic group A.\n
LOCATION:https://researchseminars.org/talk/LNTS/77/
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