Yeongseong Jo, Muthu Krishnamurthy
Published 2021-04-10Version 1
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 \`{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.
On the support of matrix coefficients of supercuspidal representations of the general linear group over a local non-archimedean field
Modular reduction of the Steinberg lattice of the general linear group
Representations of general linear groups and categorical actions of Kac-Moody algebras
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