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

Mendes, Sergio and Plymen, Roger (2014) L-packets and depth 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 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).

Item Type: MIMS Preprint
Uncontrolled Keywords: Representation theory, L-packets, depth
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
MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User: Professor Roger Plymen
Date Deposited: 03 Feb 2014
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2097

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