Abstract:We consider vertices, a notion originating in local representation theory of finite groups, for the category $\mathcal {O}$ of a rational Cherednik algebra and prove the analogue of the Dipper-Du Conjecture for Hecke algebras of symmetric groups in that setting. As a corollary we obtain a new proof of the Dipper-Du Conjecture over $\mathbb {C}$.

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中文翻译：

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重新审视 Dipper-Du 猜想

摘要：我们考虑顶点，一个源自有限群局部表示理论的概念，用于有理 Cherednik 代数的范畴 $\mathcal {O}$ 并证明对称群的 Hecke 代数的 Dipper-Du 猜想的类比环境。作为推论，我们在 $\mathbb {C}$ 上获得了 Dipper-Du 猜想的新证明。

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