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Let $G$ be an affine algebraic group with a reductive identity component $G^{0}$ acting regularly on an affine Krull scheme $X = {Spec} (R)$ over an algebraically closed field. Let $T$ be an algebraic subtorus of $G$ and suppose that ${Q}(R)^{T}= {Q}(R^{T})$ of quotient fields. We will show: If $G$ is the centralizer of $T$ in $G$, then the pseudo-reflections of the action of $G$ on $R^{T}$ can be lifted to those on $R$.

LIFTINGS OF PSEUDO-REFLECTION GROUPS OF TORIC QUOTIENTS OF KRULL SCHEMES