The Langlands-Shahidi method for pairs via types and covers

Jo, Yeongseong; Krishnamurthy, M.

doi:10.1090/ert/620

The Langlands-Shahidi method for pairs via types and covers
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by Yeongseong Jo and M. Krishnamurthy

Represent. Theory 26 (2022), 635-672

DOI: https://doi.org/10.1090/ert/620

Published electronically: June 28, 2022

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Abstract:

We compute the local coefficient attached to a pair $(\pi _1,\pi _2)$ of supercuspidal (complex) representations of the general linear group using the theory of types and covers à 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.

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