Computation of weighted Bergman inner products on bounded symmetric domains and restriction to subgroups II

Let (G, G₁) be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces D₁=G₁/K₁ D=G/K, realized as bounded symmetric domains in complex vector spaces p^+₁^+ respectively. Then the universal covering group G of G acts unitarily on the weighted Bergman space H_ (D) (D) on D. Its restriction to the subgroup G₁ decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua--Kostant--Schmid--Kobayashi's formula in terms of the K₁-decomposition of the space P (p^+₂) of polynomials on the orthogonal complement p^+₂ of p^+₁ in p^+. The object of this article is to compute explicitly the inner product f (x₂), e^ (x|z) ₏^+_ for f (x₂) ₊ (p^+₂) (p^+₂), x= (x₁, x₂), z^+=p^+₁^+₂, and to construct explicitly G₁-intertwining operators (symmetry breaking operators) H_ (D) |₆䃑䃑 (D₁, P₊ (p^+₂) ) from holomorphic discrete series representations of G to those of G₁, which are unique up to constant multiple for sufficiently large. In this article, we treat the case p^+, p^+₂ are both simple of tube type and rankp^+=rankp^+₂. When rankp^+=3, we treat all partitions k, and when rankp^+ is general, we treat partitions of the form k= (k, , k, k-l).