Branching rules for ramified principal series representations of GL(3) over a p-adic field

2007/10/17 by Peter S. Campbell, Campbell, Peter S., Monica Nevins +1
Mathematics · #20G05 #20G25 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20G05 #msc:20G25

paper · pdf · doi:10.48550/arxiv.0710.3263

18 pages

arxiv created 2007/10/17 · arxiv updated 2009/12/01

Abstract

We decompose the restriction of ramified principal series representations of the p-adic group GL(3,k) to its maximal compact subgroup K=GL(3,\mathscrR). Its decomposition is dependent on the degree of ramification of the inducing characters and can be characterized in terms of filtrations of the Iwahori subgroup in K. We establish several irreducibility results and illustrate the decomposition with some examples.

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