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Spinors and canonical hermitian forms

Published online by Cambridge University Press:  18 May 2009

P. L. Robinson
P. L. Robinson
Affiliation:
School of Mathematics, Trinity College, Dublin 2, Ireland
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The space S of spinors associated to a 2m-dimensional real inner product space (V, B) carries a canonical Hermitian form 〈 〉 determined uniquely up to real multiples. This form arises as follows: the complex Clifford algebra C(V) of (V, B) is naturally provided with an antilinear involution; this induces an involution on End S via the spin representation; this is the adjoint operation corresponding to 〈 〉.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 263 - 270
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Atiyah, M. F., Bott, R. and Shapiro, A., Clifford modules, Topology 3 (1964), Supplement, 3–38.CrossRefGoogle Scholar
2.Bourbaki, N., Algèbre, Chapitre 9 (Hermann, 1959).Google Scholar
3.Chevalley, C., The algebraic theory of spinors (Columbia University Press, 1954).CrossRefGoogle Scholar
4.Deheuvels, R., Formes quadratiques et groupes classiques (Presses Universitaires de France, 1981).Google Scholar
5.Greub, W., Multilinear algebra, second edition (Springer-Verlag Universitext, 1978).CrossRefGoogle Scholar