Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians

Based on the method by [K\"uc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles on Grassmannians for each dimension. In particular, we give a classification of such Calabi--Yau 3-folds and determine their topological invariants. We also give alternative descriptions for some of them.