Representations of general linear groups over local non-archimedean fields: old and new

Algebraic Geometry and Number Theory Seminar

Representation theory of reductive groups over local non archimedean fields goes back to Gelfand in the 1940s.
It plays a key role in the Langlands program and has a vast history. The case of the general linear group is particularly important.
It was studied in the seminal work of Bernstein--Zelevinsky in the 1970s. Later on, connections with other aspects of
representation theory, such as quantum groups, shed new light on the theory.
In this talk I will discuss some basic themes in the theory and several relatively new conjectures and results on the structure
of parabolic induction.
Partly based on joint work with A. Minguez, A. Aizenbud and M. Gurevich.
No priori familiarity with the subject will be assumed.