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Title: On the mod-ρ representations of unramified U(2,1)
Author: Xu, Peng
Awarding Body: University of East Anglia
Current Institution: University of East Anglia
Date of Award: 2014
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Let E/F be an unramified quadratic extension of non-archimedean local fields of odd residue characteristic ρ and let G be the unitary group in three variable U(2,1)(E/F). In this thesis, we explore the smooth representation theory of G over a field Ẽ of characteristic ρ. The main results are as follows. Firstly, we have classified the simple modules of the pro-ρ Iwahori-Hecke algebra of G and described the so-called supersingular ones, which is one-dimensional character. Secondly, for the hyperspecial maximal compact open subgroup K₀ of G and any irreducible smooth representation σ of K₀, and for any non-zero λεẼ, we have determined the subquotients of indG/K₀σ/(Tσ-λ) by matching them precisely with the irreducible subquotients of principal series of G, where Tλ is some Hecke operator in the spherical Hecke algebra of G with respect to K₀ and σ. The latter result confirms a conjecture of Abdellatif. We also include several results aimed towards proving that supersingular representations of G are not finitely presented.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available