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arXiv · 1806.03670

Globally analytic principal series representation and Langlands base change

Jishnu Ray
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Abstract

S. Orlik and M. Strauch have studied locally analytic principal series representation for general $p$-adic reductive groups generalizing an earlier work of P. Schneider for $GL(2)$ and related the condition of irreducibility of such locally analytic representation with that of a suitable Verma module. In this article, we take the case of $GL(n)$ and study the globally analytic principal series representation under the action of the pro-$p$ Iwahori subgroup of $GL(n,\mathbb{Z}_p)$, following the notion of globally analytic representations introduced by M. Emerton. Furthermore, we relate the condition of irreducibility of our globally analytic principal series to that of a Verma module. Finally, using Steinberg tensor product theorem, we construct Langlands base change of our globally analytic principal series to a finite unramified extension of $\mathbb{Q}_p$, generalizing an earlier work of Clozel for $GL(2)$.

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Jishnu Ray. 2018-06-10. Globally analytic principal series representation and Langlands base change. https://doi.org/10.2140/pjm.2020.307.455

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