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.
KeywordsSymmetric Group Irreducible Character Defect Group Projective Representation Minimal Height
Unable to display preview. Download preview PDF.
- 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