Quantum cohomology ring for hermitian symmetric spaces of type DIII

We determine the quantum cohomology ring for hermitian symmetric spaces of type DIM. Among the manifolds whose quantum cohomology ring has been rigorously computed, two hermitian symmetric spaces have been reported so far. The one we show in this paper, following a result of Sievert and Tian, is the third example. For this purpose encouting of the number of rational curves over the spaces satisfying a certain dimension condition is needed and it is accomplished by cell decomposition of hermitian symmetric spaces which are analogue of the Scubert cell for complex Grassmann manifolds.