The Langlands-Shahidi method for pairs via types and covers

Yeongseong Jo; Muthu Krishnamurthy

The Langlands-Shahidi method for pairs via types and covers

Representation Theory 2022-04-13 v2 Number Theory

Authors: Yeongseong Jo , Muthu Krishnamurthy

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 \`{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.

Keywords

langlands correspondence automorphic representations local-global principles

Cite

@article{arxiv.2104.04876,
  title  = {The Langlands-Shahidi method for pairs via types and covers},
  author = {Yeongseong Jo and Muthu Krishnamurthy},
  journal= {arXiv preprint arXiv:2104.04876},
  year   = {2022}
}