Heights of Spin Characters in Characteristic 2
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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- C. Bessenrodt, J. B. Olsson, The 2-blocks of the symmetric groups, Institut für Experimentelle Mathematik, Essen, Preprint No. 17 (1993).Google Scholar
- G. James, A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, 1981.Google Scholar
- J. B. Olsson, Combinatorics and Representations of Finite Groups, Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen, Heft 20, 1993.Google Scholar
- G. R. Robinson, Local Structure, Vertices and Alperin’s Conjecture. Preprint 1994Google Scholar