A remark on descent for Coxeter groups

Abstract

Let $\Gamma$ be a finite Coxeter group with reflection representation $R$. We show that a $\Gamma$-equivariant quasicoherent sheaf on $R$ descends to the quotient space $R//\Gamma$ if it descends to the quotient space $R//⟨s_i⟩$ for every simple reflection $s_i\in \Gamma$.

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