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arXiv · 2604.21619

The Representation Type of the Descent Algebras

Karin Erdmann·Kay Jin Lim
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Abstract

Schocker classified the representation type of the descent algebra of type $\mathbb{A}$ over any field of characteristic zero. In an earlier paper, the authors extended this classification for type $\mathbb{A}$ to fields of positive characteristic. In this paper, we complete the classification for all other types except for $\mathbb{E}_8$. The proof for type $\mathbb{B}$ is entirely theoretical, while some small cases in type $\mathbb{D}$ and the exceptional types require computer computation to determine their Ext-quivers.

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Karin Erdmann, Kay Jin Lim. 2026-04-23. The Representation Type of the Descent Algebras. https://arxiv.org/abs/2604.21619

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