Abstract
Let K be a complete local field which residual field is finite of characteristic p and let l be a prime number not equal to p. Given a Q ¯ l -irreducible cuspidal integral representation π, we describe, for all s ⩾ 1 , the irreducible sub-quotients of the reduction modulo l of the generalized Steinberg representation St s ( π ) . By induction and with the use of the parabolic induction, we construct then stable lattices of St s ( π ) and describe a filtration of their reduction modulo l which appears, cf. Boyer (in preparation) [4], in the description of the l-torsion of the p+-intermediate extensions of the local systems of Harris–Taylor.
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