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Projective representations of the infinite orthogonal group

Part of: Linear algebraic groups and related topics Lie groups

Published online by Cambridge University Press:  26 February 2010

R. J. Plymen
R. J. Plymen
Affiliation:
The Department of Mathematics, University of Manchester,Manchester, M13 9PL,
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Extract

Let ℝ∞ be the direct limit of the Euclidean spaces ℝn. Now the orthogonal group O(∞) acts on ℝn and the direct limit O(∞) of the groups O(∞) acts on ℝ∞. The infinite pin group Pin(∞) is an extension of ℤ2 by O(∞) and admits the following presentation: the generators are the unit vectors xf in ℝ∞ and the relations are

MSC classification

Secondary: 20G05: Representation theory 22E45: Representations of Lie and linear algebraic groups over real fields
Type
Research Article
Information
Mathematika , Volume 24 , Issue 1 , June 1977 , pp. 115 - 121
Copyright
Copyright © University College London 1977

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References

1.Atiyah, M. F, Bott, R. and Shapiro, A.. “Clifford modules ”, Topology, 3, supplement 1 (1964) 3–38.CrossRefGoogle Scholar
2.Morris, A. O.. “Projective representations of reflection groups ”, Proc. London Math. Soc. (3), 32 (1976), 403–420.Google Scholar
3.Plymen, R. J.. “Spinors in Hilbert space ”, Math. Proc. Camb. Phil. Soc, 80 (1976), 337–347.Google Scholar
4.Plymen, R. J.. “Recent results on infinite-dimensional spin groups ”, Advances in Math. To appear.Google Scholar
5.Powers, R. T..“Representations of uniformly hyperfinite algebras and the associated von Neumann rings ”, Ann. Math., 86 (1967), 138–171.Google Scholar
6.Strătilă, S. and Voiculescu, D.. Representations of AF-algebras and of the group U(¦), Lecture Notes in mathematics, 486 (Springer-Verlag, Berlin, 1975).Google Scholar
7.Atiyah, M. F. and Macdonald, I. G.. Introduction to commutative algebra (Addison-Wesley, Massachusetts, 1969).Google Scholar