Types and supercuspidal representations of p-adic symplectic groups
Shaun Stevens
Thesis, King's College London, 1998
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Abstract. 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).
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