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.
supported by a grant from the EC (Network on Algebraic Combinatorics).
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© 1997 Birkhäuser Boston
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Bessenrodt, C., Olsson, J.B. (1997). Heights of Spin Characters in Characteristic 2. In: Cabanes, M. (eds) Finite Reductive Groups: Related Structures and Representations. Progress in Mathematics, vol 141. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4124-9_3
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DOI: https://doi.org/10.1007/978-1-4612-4124-9_3
Publisher Name: Birkhäuser Boston
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