THE LANGLANDS-SHAHIDI METHOD FOR PAIRS VIA TYPES AND COVERS

We compute the local coefficient attached to a pair (π₁, π₂) of supercuspidal (complex) representations of the general linear group using the theory of types and covers ‘a la Bushnell-Kutzko. In the process, we obtain another proof of a well-known formula of Shahidi for the corresponding Plancherel constant. The approach taken here can be adapted to other situations of arithmetic interest within the context of the Langlands-Shahidi method, particularly to that of a Siegel Levi subgroup inside a classical group.