Decomposition matrices for spin characters of symmetric groups

Abstract

SynopsisMethods are developed for determining the decomposition matrices for the spin characters of the symmetric groups Sn for an odd prime p. Some general results are obtained which are non-trivial modifications of the corresponding results for ordinary characters. The methods are used to determine the decomposition matrices for 3 ≦ n ≦ ll, and p = 3 but with an interesting ambiguity in the case n = 9. The second author will deal separately with the cases p = 5, 7, 11.