Let \(F\) be a nonarchimedean local field (of any characteristic), and \(G\) be the \(F\)-points of a connected reductive group defined over \(F\). Let \(\widetilde{G}\) be a finite central extension of \(G\), i.e. \(\widetilde{G}\) is a topological group and there is a covering map \(\rho:\widetilde{G}\to G\) which is a surjective topological covering with kernel a finite subgroup of the center of \(\widetilde{G}\). Then the authors use intertwining operators to prove the Langlands quotient theorem, which classifies irreducible admissible representations as the unique irreducible quotients of parabolically induced representations, for \(\widetilde{G}\). They also show that the Langlands subrepresentation may be realized as the image of an intertwining operator. Then they extend the duality result of A.-M. Aubert [Trans. Am. Math. Soc. 347, No. 6, 2179–2189 (1995; Zbl 0827.22005)] (see also P. Schneider and U. Stuhler [Publ. Math., Inst. Hautes Étud. Sci. 85, 97–191 (1997; Zbl 0892.22012)]) to this context.
The authors gave an algebraic proof of the Langlands quotient theorem for \(\widetilde{G}\), which did not involve intertwining operators, in Part I of this paper [Glas. Mat., III. Ser. 48, No. 2, 313–334 (2013; Zbl 1304.22019)]. There they assumed that \(\mathrm{char}(F)=0\). They also observe in this paper that this algebraic proof goes through for all characteristics.