GAP CONDITIONS FOR REPRESENTATIONS OF SYMMETRICAL GROUPS

For the symmetric groups S(n) with n greater than or equal to 6 we con struct representations which satisfy a strong gap condition for the di mensions of various fixed point sets, as desired in equivariant surger y, and a condition on the isotropy groups, as used in the construction of manifolds with interesting fixed point sets. This allows us to con struct smooth actions of S(n) on sphere such that the fixed point set is exactly one point, or any given closed, stably parallelizable manif old, all of whose components have the same dimension. (C) 1997 Elsevie r Science B.V.