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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

Online
ISSN
1435-5337
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Volume 27, Issue 3

# Unramified representations of the universal central extension of SL2(𝔽q((z)))

Andrew J. Rose
Published Online: 2013-04-06 | DOI: https://doi.org/10.1515/forum-2012-0140

## Abstract

In this paper we are interested in investigating the principal series representations of a certain rank 2 Kac–Moody group. This group (denoted by ${\stackrel{˜}{\mathrm{SL}}}_{2}\left({𝔽}_{q}\left(\left(z\right)\right)\right)$) is introduced as a central extension by ${𝔽}_{q}^{*}$ of the group of two-by-two unimodular matrices over the non-archimedean local field, ${𝔽}_{q}\left(\left(z\right)\right)$. We begin by determining a formula for a cocycle that defines this central extension. This is used to classify all irreducible representations of the centrally extended torus inside ${\stackrel{˜}{\mathrm{SL}}}_{2}\left({𝔽}_{q}\left(\left(z\right)\right)\right)$ and, as a consequence of this classification, we are able to determine the irreducible unramified principal series representations of ${\stackrel{˜}{\mathrm{SL}}}_{2}\left({𝔽}_{q}\left(\left(z\right)\right)\right)$.

MSC: 20E50; 20G05; 20G44; 20E22; 19C09; 20C99

Revised: 2013-01-24

Published Online: 2013-04-06

Published in Print: 2015-05-01

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1453–1469, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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