Cuspidal Representations of Dyadic Classical Groups

Arnold, Michael (2020) Cuspidal Representations of Dyadic Classical Groups. Doctoral thesis, University of East Anglia.

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Let G be a Symplectic group or a Split Special Orthogonal group defined over a dyadic field. We begin by classifying the reductive quotients of most maximal parahoric subgroups of G so that we can explicitly describe its irreducible cuspidal depth-zero representations in terms of their local data. By a result of Blondel we compute the reducibility points of a parabolically induced representation from a cuspidal representation of a maximal Levi subgroup. These reducibility points are described by certain parameters of a spherical Hecke algebra occuring in the construction of a Bushnell-Kutzko cover. Using classical Deligne-Lusztig theory for finite reductive groups, we verify an equality due to Moeglin which (conjecturally) allows one to identify the Langlands parameter associated to an irreducible cuspidal depth-zero representation of G through the local Langlands correspondence.
We then begin an exhaustive investigation into positive-depth cuspidal representations of Sp4(F) over a dyadic field. By using both the languages of Bushnell-Kutzko and Moy-Prasad we show that any irreducible representation of Sp4(F) contains a G-fundamental stratum. We then take the first steps towards the computation of intertwining of G-fundamental strata by explicitly describing the distinguished double-coset representatives of the maximal parahoric subgroups.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Nicola Veasy
Date Deposited: 17 Mar 2021 14:33
Last Modified: 17 Mar 2021 14:33

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