An Analogue of the Ichino-Ikeda Conjecture for Whittaker Coefficients of the Metaplectic Group

A few years ago Ichino-Ikeda formulated a quantitative version of the Gross-Prasad conjecture, modeled after the classical work of Waldspurger. This is a powerful local-to-global principle which is very suitable for analytic and arithmetic applications. One can formulate a Whittaker analogue of the Ichino-Ikeda conjecture. We use the descent method of Ginzburg-Rallis-Soudry to reduce the Whittaker version to a purely local identity which we prove in the p-adic case under some mild hypotheses. Joint work with Zhengyu Mao