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arXiv:math/0605255 [math.DG]AbstractReferencesReviewsResources

Generalized Weierstrass Relations and Frobenius reciprocity

Shigeki Matsutani

Published 2006-05-10, updated 2007-03-11Version 4

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.

Comments: 17pages. to be published in Mathematical Physics, Analysis and Geometry
Categories: math.DG, math-ph, math.MP
Subjects: 53A10, 53C27, 15A66
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