Study of algebraic structure and geometric structure of Schroedinger equations on symmetric spaces

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We mainly studied the detailed structure of the fundamental solution to the Schroedinger equation on compact symmetric spaces from the point of view of number theory and representation theory. One of our main results is as follows. Under certain assumptions on the vector potential and on compact symmetric spaces, the singular support of the fundamental solution to the magnetic Schroedinger equation becomes a lower dimensional subset of the compact symmetric space, which is given in terms of generalized Gauss sums at a rational time. On the other hand, at an irrational time, the singular support of the fundamental solution coincides with the whole symmetric space.