Generalized Weierstrass Relations and Frobenius Reciprocity

This article investigates local properties of the further generalized Weierstrass relations for a spin manifold S immersed in a higher dimensional spin manifold M from viewpoint of study of submanifold quantum mechanics. We show that kernel of a certain Dirac operator defined over S, which we called submanifold Dirac operator, gives the data of the immersion. In the derivation, the simple Frobenius reciprocity of Clifford algebras S and M plays important roles.