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arXiv · 2101.04900

Typical representations, parabolic induction and the inertial local Langlands correspondence

Peter Latham
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Abstract

We prove a result which provides a link between the decomposition of parabolically induced representations and the Bushnell--Kutzko theory of typical representations. As an application, we show that there exists a well-defined inertial Langlands correspondence which respects the monodromy action of L-parameters, under some standard conjectures regarding the local Langlands correspondence. To allow for potential applications of this inertial Langlands correspondence, we also provide a complete construction of the set of typical representations, giving a parametrization of these in terms of the structure of the Bruhat--Tits building of $G$.

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Peter Latham. 2021-01-13. Typical representations, parabolic induction and the inertial local Langlands correspondence. https://arxiv.org/abs/2101.04900

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