# Modular l representations of SL_n(F)

05.11.2019 13:15 - 14:45

Peiyi Cui (University of Vienna)

Let F be a non-archimedean locally compact field of residual characteristic p, and k be an algebraically closed field of characteristic l\$\neq\$p. In the study of the category Rep_{C}(SL_n(F)) of smooth C-representations of SL_n(F), the Bernstein decomposition theorem for Rep_{C}(SL_n(F)) is based on the fact that the supercuspidal support of irreducible C-representations of Levi subgroups M of SL_n(F) is unique. In this talk, we will consider Rep_k(SL_n(F)), and show that the supercuspidal support of irreducible smooth k-representations of Levi subgroups M of SL_n(F) is unique up to M-conjugation, when F is either a finite field of characteristic p or a non-archimedean locally compact field of residual characteristic p.

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