Types and supercuspidal representations of p-adic symplectic groups

Stevens, S (1998) Types and supercuspidal representations of p-adic symplectic groups. Other thesis, King's College London.

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Let F be a non-archimedean local field and let G = G(F) be the F-points of a reductive group defined over F. Bushnell and Kutzko have described a strategy to classify the representations of G via the theory of types, which associates to each inertial class in the Bernstein spectrum a pair (K, ρ) consisting of a compact open subgroup K of G and an irreducible representation ρ of K.

We impose the restriction that the residual characteristic of F not be 2.

In this thesis we begin the construction of types associated to certain discrete series (in particular, to supercuspidal) representations of G = Sp2N(F) by transferring Bushnell and Kutzko's construction for GL2N(F) to our situation. Certain objects in the construction, in particular the simple characters, transfer simply by restriction.

In a certain case, we complete the construction of the type (K, ρ) and hence construct new supercuspidal representations in the wildly ramified case. In this case, we are also able to describe a (tentative) transfer map from certain supercuspidal representations of GL2N(F) to supercuspidal representations of Sp2N(F), which associates to each representation π of GL2N(F) a set Π(π) of representations of Sp2N(F)

Item Type: Thesis (Other)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:44
Last Modified: 20 Oct 2011 10:20
URI: https://ueaeprints.uea.ac.uk/id/eprint/21078


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