论文标题
$ a $ a $ hecke代数II的Schurian Finitity
Schurian-finiteness of blocks of type $A$ Hecke algebras II
论文作者
论文摘要
对于任何代数$ a $，代数封闭的字段$ \ mathbb {f} $，我们说如果$ a $ a-module $ m $是schurian，则如果$ \ mathrm {end} _a（m）_a（m）\ cong \ cong \ mathbb {f} $。我们说$ a $是Schurian-Finite，如果只有许多同构的schurian $ a $ modules和Schurian-Infinite的同构类别。在本文中，我们建立在Ariki的工作和第二位作者的基础上，以表明所有类型的$ a $ a $ hecke重量代数至少$ 2 $ $ 2 $的量子特征$ e \ geq 3 $ is schurian-infinite。这证明，如果$ e \ e \ geq 3 $，则$ a $ a $ hecke代数的块是schurian-finite，并且仅当它们为代表时。
For any algebra $A$ over an algebraically closed field $\mathbb{F}$, we say that an $A$-module $M$ is Schurian if $\mathrm{End}_A(M) \cong \mathbb{F}$. We say that $A$ is Schurian-finite if there are only finitely many isomorphism classes of Schurian $A$-modules, and Schurian-infinite otherwise. In this paper, we build on the work of Ariki and the second author to show that all blocks of type $A$ Hecke algebras of weight at least $2$ in quantum characteristic $e \geq 3$ are Schurian-infinite. This proves that if $e \geq 3$ then blocks of type $A$ Hecke algebras are Schurian-finite if and only if they are representation-finite.
