Types and supercuspidal representations of p-adic symplectic groups

Let <i>F</i> be a non-archimedean local field and let <i>G</i> = <b>G</b>(<i>F</i>) be the <i>F</i>-points of a reductive group defined over <i>F</i>. Bushnell and Kutzko have described a strategy to classify the representations of <i>G</i> via the theory of types, which associates to each inertial class in the Bernstein spectrum a pair (<i>K</i>, ρ) consisting of a compact open subgroup <i>K</i> of <i>G</i> and an irreducible representation ρ of <i>K</i>. <p> We impose the restriction that the residual characteristic of <i>F</i> not be 2. <p> In this thesis we begin the construction of types associated to certain discrete series (in particular, to supercuspidal) representations of <i>G</i> = Sp_2<i>N</i>(<i>F</i>) by transferring Bushnell and Kutzko's construction for GL_2<i>N</i>(<i>F</i>) to our situation. Certain objects in the construction, in particular the simple characters, transfer simply by restriction. <p> In a certain case, we complete the construction of the type (<i>K</i>, 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 GL_2<i>N</i>(<i>F</i>) to supercuspidal representations of Sp_2<i>N</i>(<i>F</i>), which associates to each representation π of GL_2<i>N</i>(<i>F</i>) a set Π(π) of representations of Sp_2<i>N</i>(<i>F</i>)</p></p></p>

Name dc:type.qualificationname

other

Level dc:type.qualificationlevel

other

Grantor dc:publisher.institution

King's College London

Year dc:date.issued

1998

Author dc:creator

• Stevens, S

Language dc:language

en

Repository record dc:identifier.uri

https://ueaeprints.uea.ac.uk/id/eprint/21078/1/thesis.dvi

OAI identifier oai:identifier

oai:ueaeprints.uea.ac.uk:21078