The theta correspondence over finite fields
Abstract
This set of lecture notes is an expanded version of a mini-course the author gave in March of 2025 for the program ``Representation Theory \& Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris. The goal is to provide a survey of the main properties of the theta correspondence over finite fields of odd characteristic, including its compatibility with Harish-Chandra and Lusztig series, and with the Jordan decomposition of representations, as well as its full explicit description.
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