Trace ideals of canonical modules over Schubert cycles and determinantal rings

In this paper, we study the canonical trace of Schubert cycles and determinantal rings. As an application, we give an explicit description of the non-Gorenstein locus and show that its structure is compatible with the known representations of the singular locus and the canonical module. Furthermore, for the CTR property recently introduced by Miyazaki, we establish its stability under base change and provide a characterization in the case of determinantal rings.