No abstract

In this paper, we present, given a odd integer d, a decomposition of the multiset of bar lengths of a bar partition λ as the union of two multisets, one consisting of the bar lengths in itsd-core partition c d (λ) and the other consisting of modified bar lengths in itsd-quotient partition. In particular, we obtain that the multiset of bar lengths in c d (λ) is a sub-multiset of the multiset of bar lengths in λ. Also, we obtain a relative bar formula for the degrees of spin characters of the Schur extensions of Sn. The proof involves a recent similar result for partitions, proved in [1].