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arXiv · 1402.0184

L-packets and depth for SL_2(K) with K a local function field of characteristic 2

Sergio Mendes·Roger Plymen
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Abstract

Let G = SL_2(K) with K a local function field of characteristic 2. We review Artin-Schreier theory for the field K, and show that this leads to a parametrization of certain L-packets in the smooth dual of G. We relate this to a recent geometric conjecture. The L-packets in the principal series are parametrized by quadratic extensions, and the supercuspidal L-packets of cardinality 4 are parametrized by biquadratic extensions. Each supercuspidal packet of cardinality 4 is accompanied by a singleton packet for SL_1(D). We compute the depths of the irreducible constituents of all these L-packets for SL_2(K) and its inner form SL_1(D).

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BibTeXRIS

Sergio Mendes, Roger Plymen. 2014-02-02. L-packets and depth for SL_2(K) with K a local function field of characteristic 2. https://arxiv.org/abs/1402.0184

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