The sparsity of character tables over finite reductive groups and its additive analogue

2025/12/05 by Nam, GyeongHyeon, Puskás, Anna
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.05773

Abstract

We consider the proportion of zero entries in the character table of a sequence of reductive groups over a finite field. We prove an asymptotic lower bound when the reductive group is fixed and the size of the finite field increases. Furthermore, we prove that when considering a sequence of reductive groups with increasing semisimple rank, the proportion is asymptotically one. We also establish an additive analogue of this phenomenon in the context of a fixed reductive Lie algebra.

Citations

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• Rank and Duality in Representation Theory