Heights of spin characters in characteristic 2
Séminaire lotharingien de combinatoire, Tome 34 (1995)
Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website
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.
@article{SLC_1995_34_a2,
author = {Christine Bessenrodt and J.B. Olsson},
title = {Heights of spin characters in characteristic 2},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {34},
year = {1995},
url = {http://geodesic.mathdoc.fr/item/SLC_1995_34_a2/}
}
Christine Bessenrodt; J.B. Olsson. Heights of spin characters in characteristic 2. Séminaire lotharingien de combinatoire, Tome 34 (1995). http://geodesic.mathdoc.fr/item/SLC_1995_34_a2/