Generalized Weierstrass Relations and Frobenius reciprocity
arXiv:math/0605255 · doi:10.1007/s11040-007-9016-5
Abstract
This article investigates local properties of the further generalized Weierstrass relations for a spin manifold immersed in a higher dimensional spin manifold from viewpoint of study of submanifold quantum mechanics. We show that kernel of a certain Dirac operator defined over , which we call submanifold Dirac operator, gives the data of the immersion. In the derivation, the simple Frobenius reciprocity of Clifford algebras and plays important roles.
17pages. to be published in Mathematical Physics, Analysis and Geometry