Abstract
A spinor, first introduced by E. Cartan [1], is an element of the vector space on which a certain representation of the orthogonal Lie algebra operates. This representation is called the spin representation, the group it represents is called the spin group. The significance of the theory of spinors has long been recognized by its application in mathematics as well as in the mathematical modeling of many physical phenomena. In this paper we shall summarize some results on the classification of spinors under the even Clifford group GSpin m , over archimedean as well as finite fields of characteristic different from 2. Specifically, we shall exhibit
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(1)
the decomposition of the space of spinors into GSpin m -equivalence classes or “orbits”, and
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(2)
the structure of the stabilizer of GSpin m for each orbit.
supported in part by the National Security Agency grant MDA904-90-H-4038.
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References
E. Cartan, “Lecons sur la Theorie de Spineurs”, Paris: Hermann et Cie. (1938).
E. Cartan, “The Theory of Spinors”, Massachusetts Institute of Technology Press (1966).
C. Chevalley, “The Algebraic Theory of Spinors”, Columbia University Press (1954).
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V. L. Popov, “Classification of Spinors of Dimension Fourteen”, Trans. Moscow Math. Soc. 1 (1980) p.181–232.
M. Sato and T. Kimura, “A Classification of Irreducible Prehomogeneous Vector Spaces and Their Relative Invariants’, Nagoya Math. J. 65 (1977) p. 1–155.
X. W. Zhu, “The Classification of Spinors under GSpin14 over Finite Fields”, to appear in Transaction of American Mathematical Society.
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© 1992 Springer Science+Business Media Dordrecht
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Zhu, XW. (1992). On spinor classifications. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_18
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DOI: https://doi.org/10.1007/978-94-015-8090-8_18
Publisher Name: Springer, Dordrecht
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