We establish scale-invariant Strichartz estimates for the Schrödinger flow on any compact
Lie group equipped with canonical rational metrics. In particular, full Strichartz estimates
without loss for some nonrectangular tori are given. The highlights of this paper include
estimates for some Weyl-type sums defined on rational lattices, different decompositions
of the Schrödinger kernel that accommodate different positions of the variable inside the
maximal torus relative to the cell walls, and an application of the BGG-Demazure operators
or Harish-Chandra’s integral formula to the estimate of the difference between characters.
Keywords
compact Lie groups, Schrödinger equation, circle method,
Strichartz estimates, BGG-Demazure operators,
Harish-Chandra's integral formula
