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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 $\mathbb{C}$.