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SUMMARY:Decompositions of the category of l-modular representations of SL_
 n(F). - Peiyi Cui (University of East Anglia)
DTSTART:20230131T143000Z
DTEND:20230131T153000Z
UID:TALK195358@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:Let F be a p-adic field\, and k an algebraically closed field 
 of characteristic l different from p. In this talk\, we will first give a 
 category decomposition of Rep_k(SL_n(F))\, the category of smooth k-repres
 entations of SL_n(F)\, with respect to the GL_n(F)-equivalent supercuspida
 l classes of SL_n(F)\, which is not always a block decomposition in genera
 l. We then give a block decomposition of the supercuspidal subcategory\, b
 y introducing a partition on each GL_n(F)-equivalent supercuspidal class t
 hrough type theory\, and we interpret this partition by the sense of l-blo
 cks of finite groups. We give an example where a block of Rep_k(SL_2(F)) i
 s 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 g
 iving a prediction on the block decomposition of Rep_k(A) for a general p-
 adic group A.
LOCATION:MR13
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