Reductive dual pair

A reductive dual pair is a concept that arises in the context of representation theory and Lie groups. Specifically, it refers to a pair of reductive algebraic groups (or Lie groups) that have compatible structures allowing for the decomposition of representations in a certain way. The term is primarily used in the study of harmonic analysis on groups and has implications in various fields, including number theory, geometry, and mathematical physics. ### Key Points 1.