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Journal of the London Mathematical Society 1991 s2-43(3):412-420; doi:10.1112/jlms/s2-43.3.412
© 1991 by London Mathematical Society
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© Oxford University Press

Real Projective Representations of Clifford Algebras, and Symmetric Groups

M. K. Makhool and A. O. Morris

Department of Mathematics, The University College of Wales Aberystwyth, Dyfed SY23 3BZ

In earlier publications, the second author has shown how a Clifford-algebra approach could be used to determine results concerning the complex covering groups of reflection groups and, in particular, symmetric groups. More recently, M. L. Nazarov [7, 8] has shown how to determine a complete set of irreducible projective representations of symmetric groups. Our main aim in this paper is to extend all of these results to the real case. Surprisingly, the background explicit information about the real representations of Clifford algebras and the real covering groups of orthogonal groups were not available.


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