On $L$-packets and depth for $SL_2(K)$ and its inner form

Anne-Marie Aubert; Sergio Mendes; Roger Plymen; Maarten Solleveld

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arXiv · 1610.02645

On $L$-packets and depth for $SL_2(K)$ and its inner form

Anne-Marie Aubert·Sergio Mendes·Roger Plymen·Maarten Solleveld

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Abstract

We consider the group $SL_2(K)$, where $K$ is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of $SL_2 (K)$ is larger than the depth of the corresponding Langlands parameter, with equality if and only if the L-parameter is essentially tame. We also work out a classification of all $L$-packets for $SL_2 (K)$ and for its non-split inner form, and we provide explicit formulae for the depths of their $L$-parameters.

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BibTeX RIS

Anne-Marie Aubert, Sergio Mendes, Roger Plymen, Maarten Solleveld. 2016-10-09. On $L$-packets and depth for $SL_2(K)$ and its inner form. https://arxiv.org/abs/1610.02645

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