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Projective representations of rotation subgroups of Weyl groups

Published online by Cambridge University Press:  24 October 2008

D. Theo
D. Theo
Affiliation:
Department of Mathematics, University of Zambia, Lusaka, Zambia
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Extract

By exploiting the well known spin representations of the orthogonal groups O(l), Morris [12] was able to give a unified construction of some of the projective representations of Weyl groups W(Φ) which had previously only been available by ad hoc means [5]. The principal purpose of the present paper is to give a corresponding construction for projective representations of the rotation subgroups W+(Φ) of Weyl groups. Thus we construct non-trivial central extensions of W+(Φ) via the well-known double coverings of the rotation groups SO(l). This adaptation allows us to give a unified way of obtaining the basic projective representations of W+(Φ) from those of W(Φ) determined in [12]. Hence our work is a development of the recent work of Morris, and is an extension of Schur's work on the alternative groups [15].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 21 - 35
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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