Generalized Weierstrass Relations and Frobenius reciprocity

Details Generalized Weierstrass Relations and Frobenius reciprocity Generalized Weierstrass Relations and Frobenius reciprocity

2006-05-10

arxiv.org/abs/math/0605255v4

Mathematics

Differential Geometry

17pages. to be published in Mathematical Physics, Analysis and Geometry

Scientific paper

10.1007/s11040-007-9016-5

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 call 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.

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