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University of Cambridge > Talks.cam > Number Theory Seminar > Decompositions of the category of l-modular representations of SL_n(F).

## Decompositions of the category of l-modular representations of SL_n(F).Add to your list(s) Download to your calendar using vCal - Peiyi Cui (University of East Anglia)
- Tuesday 31 January 2023, 14:30-15:30
- MR13.
If you have a question about this talk, please contact Rong Zhou. 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-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 block decomposition of the supercuspidal subcategory, by introducing a partition on each GL_n(F)-equivalent supercuspidal class through type theory, and 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. This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
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