2024/01/28 by Sambale, Benjamin · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2401.15706
We consider complex characters of a p-group P, which are invariant under a fusion system F on P. Extending a theorem of Bárcenas--Cantarero to non-saturated fusion systems, we show that the number of indecomposable F-invariant characters of P is greater or equal than the number of F-conjugacy classes of P. We further prove that these two quantities coincide whenever F is realized by a p-solvable group. On the other hand, we observe that this is false for constrained fusion systems in general. Finally, we construct a saturated fusion system with an indecomposable F-invariant character, which is not a summand of the regular character of P. This disproves a recent conjecture of Cantarero--Combariza.