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

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

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

Representation Theory 2019-01-28 v1

Authors: Anne-Marie Aubert , Sergio Mendes , Roger Plymen , Maarten Solleveld

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.

Keywords

langlands correspondence

Cite

@article{arxiv.1610.02645,
  title  = {On $L$-packets and depth for $SL_2(K)$ and its inner form},
  author = {Anne-Marie Aubert and Sergio Mendes and Roger Plymen and Maarten Solleveld},
  journal= {arXiv preprint arXiv:1610.02645},
  year   = {2019}
}

Comments

22 pages. This article supercedes arXiv:1402.0184 and arXiv:1302.6038

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

Abstract

Keywords

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