On p-quotients for spin characters (Q1262389)

It is a well-known combinatorial fact [see \textit{G. D. James} and \textit{A. Kerber}, The representation theory of the symmetric group (Addison- Wesley, 1981; Zbl 0491.20010)] that given positive integers p, n a partition \(\lambda\) of n is uniquely determined by its p-core \(\lambda_{(p)}\) and its p-quotient \(\lambda^{(p)}\). An analogue of the result of \textit{H. Farahat} [Proc. Lond. Math. Soc., III. Ser. 4, 303- 316 (1954; Zbl 0058.259)] is proved for the spin characters of the covering groups \(\hat S_ n\) of \(S_ n\).