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.
Bibliographical noteFunding Information:
The ﬁrst author would like to thank R. Ye and E. Zelingher for a very helpful discussion about the choice of the additive character. The second author would like to thank Phil Kutzko for many helpful discussions regarding this paper. Finally, we thank the anonymous referee for their useful comments.
© 2022. American Mathematical Society
- epsilon factors
- local coeﬃcients
- Types and covers