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arXiv · 2512.05773

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

GyeongHyeon Nam·Anna Puskás
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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.

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GyeongHyeon Nam, Anna Puskás. 2025-12-05. The sparsity of character tables over finite reductive groups and its additive analogue. https://arxiv.org/abs/2512.05773

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