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

Sergio Mendes; Roger Plymen

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arXiv · 1302.6038

L-packets and formal degrees 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 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 by biquadratic extensions. We compute the formal degrees of the elements in the supercuspidal packets.

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BibTeX RIS

Sergio Mendes, Roger Plymen. 2013-02-25. L-packets and formal degrees for SL_2(K) with K a local function field of characteristic 2. https://arxiv.org/abs/1302.6038

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