THE COHOMOLOGY GROUP ASSOCIATED WITH JACOBI CUSP FORMS OVER CAYLEY NUMBERS

We consider the cohomology group associated with Jacobi cusp forms ove r Cayley numbers as an example of the general theory of the cohomology groups associated with cusp forms developed by Eichler and Shimura. T he theory establishes isomorphisms between the cohomology groups and t he vector spaces of vector-valued cusp forms and then expresses their common dimensions in terms of certain geometric invariants in the corr esponding quotient spaces. This is an analogue of the Riemann-Roch the orem applied to the cases of vector-valued modular forms.