Packets and the fine structure of L-functions

Abstract: Automorphic representations, which provide a vast generalization of modular forms, are are grouped together into so-called L-packets according to the L-functions they produce. From this point of view, automorphic representations give a kind of fine-structure to L-functions themselves. While L-packets of automorphic representations are natural from this point of view, they have some deficiencies when one looks for how L-functions transfer between different groups that are related by what we call “functoriality” in the Langlands program. To address these deficiencies, Arthur introduced A-packets of automorphic representations; each A-packet is an enlarged L-packet. However, A-packets have not been defined in the same generality as L-packets. In this talk I will review this story and sketch work by my research group on a generalization of A-packets. The talk includes comments on applications of A-packets to number theory, some of which are highly speculative.

commutative algebraalgebraic geometryalgebraic topologycombinatoricsgroup theorynumber theoryrings and algebrasrepresentation theory

Audience: researchers in the topic

Calgary Algebra and Number Theory Seminar

Series comments: This seminar series is partially supported by the Pacific Institute for the Mathematical Sciences (PIMS).