A generating operator for Rankin-Cohen Brackets. 29th Nordic Congress of Mathematicians with EMS. Aalborg, Denmark, 3-7 July 2023.

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.

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© Toshiyuki Kobayashi