Strichartz estimates for the Schrödinger flow on compact Lie groups

Abstract

Every connected compact Lie group is the quotient by a finite central subgroup of a product of circles and compact simply connected simple Lie groups. Let each of the circles be equipped with a constant metric, and each of the simple groups be equipped a metric that is a constant multiple of the negative of the Cartan-Killing form, under the requirement that the periods of the Schrodinger flow on each component are rational multiples of each other. This metric on the covering group is pushed down to a metric on the original group, which is called a rational metric. This paper establishes scaling invariant Strichartz estimates for the Schrodinger flow on compact Lie groups equipped with rational metrics. The highlights of this paper include a Weyl differencing technique for rational lattices, the different decompositions of the Schrodinger kernel that accommodate different positions of the variable inside the maximal torus relative to the Weyl chamber walls, and the application of the BGG-Demazure operators to the estimate of the difference between characters.