He demenstrates some properties of schubert submodules including the fact that an integrable highest - weight module v is a union of it ' s schubert submodules and the dimensions of schubert submodules are finite although the integrable highest - weight module itself is infinite - dimensional . it ' s the purpose to find an expression to dimensions of schubert submodules in this part . this part is oganized as follows : chapter 1 is an introduction Hall在他的博士论文中，已经讨论过schubert伸和可积最高权模之间所具有的紧密联系，包括可积最高权模可表成schubert子模的并；且尽管可积最高权模的维数本身是无限的，但schubert子模的维数总是有限的；等等。
