The Representation Type of the Descent Algebras of Type A
Abstract
We classify the representation type of the descent algebras of type in the positive characteristic case. The algebras have finite representation type only for a few small degrees; otherwise, they are wild. Our main reduction method relies on a surjective algebra homomorphism from a descent algebra of type to another of lower degree. For small degree cases, we employ techniques from the representation theory of finite-dimensional algebras.
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