论文标题
Coxeter判别地层的启示剂决定因素
The Saito determinant for Coxeter discriminant strata
论文作者
论文摘要
令$ w $为有限的高级汽车组，其反射表示。 Orbit Space $ \ Mathcal {M} _W = V/W $具有显着的saito平面度量，定义为$ w $ invariant biinear biinear form $ g $的谎言衍生物。我们发现，在$ \ Mathcal {M} _W $中，intrico公制的决定因素仅限于任意的Coxeter判别层。结果表明，该决定因素与层上$ g $的平面坐标中的线性因子的产物成正比。我们还发现这些因素的多重性是从层的Coxeter几何形状方面。 该结果可以解释为对集团$ W $的Jacobian的Coxeter分解公式的判别层的概括。作为另一种解释，我们发现了地层上自然的Frobenius结构中Euler Vector Field乘法的乘法的决定因素。
Let $W$ be a finite Coxeter group and $V$ its reflection representation. The orbit space $\mathcal{M}_W= V/W$ has the remarkable Saito flat metric defined as a Lie derivative of the $W$-invariant bilinear form $g$. We find determinant of the Saito metric restricted to an arbitrary Coxeter discriminant stratum in $\mathcal{M}_W$. It is shown that this determinant is proportional to a product of linear factors in the flat coordinates of the form $g$ on the stratum. We also find multiplicities of these factors in terms of Coxeter geometry of the stratum. This result may be interpreted as a generalisation to discriminant strata of the Coxeter factorisation formula for the Jacobian of the group $W$. As another interpretation, we find determinant of the operator of multiplication by the Euler vector field in the natural Frobenius structure on the strata.
