The road to GGP (Q2111351)

The Gan-Gross-Prasad conjecture connects a problem in representation theory -- the branching law -- to arithmetic data (the \(\varepsilon\)-factor and \(L\)-value associated to the representations). This note recounts the story of how the author came up with these connections with his collaborators Prasad and Gan, with the influences of many other mathematicians. The story started with the author's work with Zagier on derivative of \(L\)-functions, and his chance interaction with Waldspurger who was a PhD student at the time. The rest of the story has fewer surprises, with the most important incident probably being a letter from India sent by Prasad. This note gives an insider's look at how important mathematical ideas are formed. It showcases the importance of idea sharing among the mathematical community, and how internet makes such idea sharing much more efficient. While Gan-Gross-Prasad formulates the conjectures, the author credits contribution from Waldspurger, Vogan, Rallis, Wallach and many others.