Generalized Weierstrass Relations and Frobenius Reciprocity |
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Authors: | Shigeki Matsutani |
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Affiliation: | (1) 8-21-1 Higashi-Linkan, 228-0811 Sagamihara, Japan |
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Abstract: | 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 the viewpoint of the study of submanifold quantum mechanics. We show that the kernel of a certain Dirac operator defined over S, which we call a submanifold Dirac operator, gives the data of the immersion. In the derivation, the simple Frobenius reciprocity of Clifford algebras S and M plays an important role. |
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Keywords: | Generalized Weierstrass relation Frobenius reciprocity |
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