Paskunas, Vytautas and Stevens, Shaun (2008) On the realisation of maximal simple types and epsilon factors of pairs. American Journal of Mathematics, 130 (5). pp. 12111261. ISSN 00029327
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Abstract
Let G be the group of rational points of a general linear group over a nonarchimedean local field F. We show that certain representations of open, compactmodcentre subgroups of G, (the maximal simple types of Bushnell and Kutzko) can be realized as concrete spaces. In the level zero case our result is essentially due to Gel'fand. This allows us, for a supercuspidal representation p of G, to compute a distinguished matrix coefficient of p. By integrating, we obtain an explicit Whittaker function for p. We use this to compute the epsilon factor of pairs, for supercuspidal representations p1, p2 of G, when p1 and the contragredient of p2 differ only at the "tame level" (more precisely, p1 and p2? contain the same simple character). We do this by computing both sides of the functional equation defining the epsilon factor, using the definition of Jacquet, PiatetskiiShapiro, Shalika. We also investigate the behaviour of the epsilon factor under twisting of p1 by tamely ramified quasicharacters. Our results generalise the special case p1=p2? totally wildly ramified, due to Bushnell and Henniart.
Item Type:  Article 

Faculty \ School:  Faculty of Science > School of Mathematics 
UEA Research Groups:  Faculty of Science > Research Groups > Algebra and Combinatorics Faculty of Science > Research Groups > Number Theory (former  to 2017) 
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Depositing User:  Vishal Gautam 
Date Deposited:  18 Mar 2011 14:44 
Last Modified:  16 May 2023 00:36 
URI:  https://ueaeprints.uea.ac.uk/id/eprint/20953 
DOI:  10.1353/ajm.0.0022 
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