Introduction

Since we have explained the background and the motivation of the study in Preface, we will explain our problems and results, which are actually investigated in this monograph.

In Section 1.1, we explain the problems. In Section 1.2, we discuss the main issues for construction of invariants. In Section 1.3, transition formulas are stated under an assumption which makes the problems much simpler. They are enough for the study of invariants in the rank 2 case, and the results are explained in Section 1.4. Generalization to the higher rank case is discussed in Section 1.5. We explain how to use master spaces for our problems in Section 1.6.