Séminaire Lotharingien de Combinatoire, B34c (1995), 22pp.
Christine Bessenrodt, J.B. Olsson
Heights of spin characters in characteristic 2
Abstract.
Based on our earlier description of the distribution into 2-blocks
of the spin characters of the covering groups of symmetric groups
we compute the heights of such characters in the blocks
containing them. We also give a complete set of labels for the spin
characters of minimal height in a 2-block.
Another related topic treated here is the determination of the minimal
power of 2 dividing a spin character degree and the explicit description
of the labels of spin characters with this minimal power of 2 in their
degree.
Also, an upper bound for the heights of spin characters in 2-blocks
is derived, and the labels of spin characters attaining this bound are
described.
As an application of our results we show that the 2-blocks of the covering
groups of symmetric groups provide further evidence for some important
representation theoretical conjectures.
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