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arXiv · 2305.19816

Minimal heights and defect groups with two character degrees

Gunter Malle·Alexander Moretó·Noelia Rizo
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Abstract

Conjecture A of \cite{EM14} predicts the equality between the smallest positive height of the irreducible characters in a $p$-block of a finite group and the smallest positive height of the irreducible characters in its defect group. Hence, it can be seen as a generalization of Brauer's famous height zero conjecture. One inequality was shown to be a consequence of Dade's Projective Conjecture. We prove the other, less well understood, inequality for principal blocks when the defect group has two character degrees.

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Gunter Malle, Alexander Moretó, Noelia Rizo. 2023-05-31. Minimal heights and defect groups with two character degrees. https://arxiv.org/abs/2305.19816

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