No abstract

Let F be a non-Archimedean locally compact field, q be the cardinality of its residue field, and R be an algebraically closed field of characteristic not dividing q. We classify all irreducible smooth R-representations of GLnpFq having a nonzero GLn¡1pFq-invariant linear form, when q is not congruent to 1 mod . Partial results in the case when q is 1 mod show that, unlike the complex case, the space of GLn¡1pFq-invariant linear forms has dimension 2 for certain irreducible representations.

Let F be a non-Archimedean locally compact field, q be the cardinality of its residue field, and R be an algebraically closed field of characteristic ℓ not dividing q. We classify all irreducible smooth R-representations of GLnpFq having a nonzero GLn´1pFq-invariant linear form, when q is not congruent to 1 mod ℓ. Partial results in the case when q is 1 mod ℓ show that, unlike the complex case, the space of GLn´1pFq-invariant linear forms has dimension 2 for certain irreducible representations.