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The Clifford algebra in dimension d = 2 m + I -1, m>2, is treated using the finite mdimensional projective geometry PG(m,2) over the field of order 2. The incidence properties of the geometry help in the problem of finding a complete commuting set of operators with which to label the 2 (d -1)/2 spinor states of an irreducible representation. Full details are given in the case m = 3, d = 15, thus generalizing previous work for the m = 2, d = 7 case, and various conjectures are made concerning the cases m> 3.

Wigner's classification of irreducible corepresentations into three types is generalised to irreducible multiplier corepresentations. Representations of Types I, II, and III have commutants isomorphic to R, H, and C, respectively. The more general problem of relating irreducible multiplier corepresentations of a group to those of an invariant subgroup is considered, and some algebraic aspects of "generalized inducing" are described. The Wigner classification is then re-obtained as a very simple instance of the general theory.

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