论文标题
仿射韦尔组和伪反射组的粗糙商
The coarse quotient for affine Weyl groups and pseudo-reflection groups
论文作者
论文摘要
我们研究了粗糙的$ \ mathfrak {t}^*// w^{\ text {aff}} $的offine weyl grout $ w^{\ text {aff}} $作用于双cartan $ \ mathfrak {t}^$的双cartan $ \ mathfrak {t}^$。具体而言，我们通过“下降”标准在此空间上对束带进行分类，该标准说$ w^{\ text {aff}} $ - 在$ \ mathfrak {t}^*$上的e earivariant sheaf the the Coveritient the Coveritient，并且只有在每个现场值下的纤维中，均为相关的点均为相关的gitients to the vereient the verients to the verients to giterient。我们还证明了作用于矢量空间的任意有限群的下降的类似定位标准。使用此情况，我们表明，当且仅当它降至每种伪反射的相关GIT商时，且仅当它降低了lonergan的最新结果时，就会出现有限的伪反射组的作用时造成的模棱两可的捆绑。
We study the coarse quotient $\mathfrak{t}^*//W^{\text{aff}}$ of the affine Weyl group $W^{\text{aff}}$ acting on a dual Cartan $\mathfrak{t}^*$ for some semisimple Lie algebra. Specifically, we classify sheaves on this space via a "pointwise" criterion for descent, which says that a $W^{\text{aff}}$-equivariant sheaf on $\mathfrak{t}^*$ descends to the coarse quotient if and only if the fiber at each field-valued point descends to the associated GIT quotient. We also prove the analogous pointwise criterion for descent for an arbitrary finite group acting on a vector space. Using this, we show that an equivariant sheaf for the action of a finite pseudo-reflection group descends to the GIT quotient if and only if it descends to the associated GIT quotient for every pseudo-reflection, generalizing a recent result of Lonergan.
