We compute the Schneider-Vigneras functor attaching a module over the Iwasawa algebra $\Lambda(N_0)$ to a $B$-representation for irreducible modulo $p$ principal series of the group $\mathrm{GL}_n(F)$ for any finite field extension $F|\mathbb{Q}_p$. It turns out to be a finitely generated module with rank 1 over $\Lambda(N_0)/\pi\Lambda(N_0)$.
Extended quotients in the principal series of reductive p-adic groups
Geometric structure in the principal series of the p-adic group G_2
Holomorphic extension of representations: (I) automorphic functions
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