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Spinors and canonical hermitian forms

  • P. L. Robinson (a1)

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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 〈 〉.

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References

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1.Atiyah, M. F., Bott, R. and Shapiro, A., Clifford modules, Topology 3 (1964), Supplement, 338.
2.Bourbaki, N., Algèbre, Chapitre 9 (Hermann, 1959).
3.Chevalley, C., The algebraic theory of spinors (Columbia University Press, 1954).
4.Deheuvels, R., Formes quadratiques et groupes classiques (Presses Universitaires de France, 1981).
5.Greub, W., Multilinear algebra, second edition (Springer-Verlag Universitext, 1978).

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