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

Mendes, Sergio and Plymen, Roger (2013) L-packets and formal degrees for SL_2(K) with K a local function field of characteristic 2. [MIMS Preprint]

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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.

Item Type: MIMS Preprint
Uncontrolled Keywords: Local function field, characteristic 2, formal degrees, special linear group, L-packets
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory
MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Professor Roger Plymen
Date Deposited: 11 Feb 2013
Last Modified: 20 Oct 2017 14:13
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1940

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