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Journal of the London Mathematical Society 1987 s2-35(3):539-550; doi:10.1112/jlms/s2-35.3.539
© 1987 by London Mathematical Society
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© Oxford University Press

Stiefel–Whitney Classes for Representations of Groups

Jeremy Gunawardena

Trinity College Cambridge CB2 1TQ

Associated to a compact Lie group G is the abelian group P(G) of total Stiefel–Whitney classes of representations. In certain cases the rank of P(G) is equal to the number of conjugacy classes of involutions in G. For the symmetric groups Sn, the total Stiefel–Whitney class of the regular representation is highly divisible in P(Sn) and this implies the existence of ‘global’ Dickson invariants in H*(BSn; F2).


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