Number Theory Seminar - Elad Zelingher

October 10, 2018
Monday, October 22, 2018 - 4:15pm to 5:15pm
Math Tower 154
Number Theory Seminar

Title: Exterior square gamma factors for cuspidal representations of $\mathrm{GL}_n$

SpeakerElad Zelingher (Yale University)

Abstract: In 1990 Jacquet and Shalika defined a family of local integrals forming an integral representation of the local exterior square $L$ function of a generic irreducible representation of $\mathrm{GL}_n \left( F \right)$, where $F$ is a local non-archimedean field of characteristic zero. Later Cogdell and Matringe showed that these integrals satisfy functional equations, which allows one to define the local exterior square factors of a generic irreducible representation of $\mathrm{GL}_n \left( F \right)$. In this talk, we define analogs of the Jacquet-Shalika integrals for irreducible cuspidal representations of $\mathrm{GL}_n \left( \mathbb{F}_q \right)$, and discuss the functional equations they satisfy. We define the exterior square gamma factor for such representation and express it using the Bessel function associated with the representation. We relate our analogs of the Jacquet-Shalika integrals to the local integrals using level zero representations. If time permits, we will also discuss our work on the local exterior square factors of simple supercuspidal representations. This is joint work with Rongqing Ye.

Seminar URLhttps://research.math.osu.edu/numbertheory/

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