We discuss recent topics on branching problems for infinite-dimensional representations of reductive groups.We plan to explain the general theory of the restriction of "small" infinite-dimensional representations, and try to present it accessible to non-experts through elementary examples.
Furthermore, we bring a new idea about what we call "generating operator" for a family of differential operators between two manifolds, and illustrate the idea for the Rankin-Cohen brackets through higher-dimensional residue calculus.
© Toshiyuki Kobayashi