# Strichartz estimates for the Schr\"odinger flow on compact Lie groups

## TL;DR

This paper proves scale-invariant Strichartz estimates for the Schr"odinger flow on compact Lie groups, including non-rectangular tori, using advanced harmonic analysis techniques and character estimates.

## Contribution

It introduces new Strichartz estimates on compact Lie groups with rational metrics, extending previous results to non-rectangular tori and employing novel analytical methods.

## Key findings

- Establishes scale-invariant Strichartz estimates on compact Lie groups.
- Provides full Strichartz estimates without loss for certain non-rectangular tori.
- Develops estimates for Weyl type sums and uses character analysis techniques.

## Abstract

We establish scale-invariant Strichartz estimates for the Schr\"odinger flow on any compact Lie group equipped with canonical rational metrics. In particular, full Strichartz estimates without loss for some non-rectangular tori are given. The highlights of this paper include estimates for some Weyl type sums defined on rational lattices, different decompositions of the Schr\"odinger 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.