For an irreducible complex reflection group $W$ of rank $n$ containing $N$ reflections, we put $g=2N∕n$ and construct a ${(g+1)}^n$-dimensional irreducible representation of the Cherednik algebra which is (as a vector space) a quotient of the diagonal coinvariant ring of $W$. We propose that this representation of the Cherednik algebra is the single largest representation bearing this relationship to the diagonal coinvariant ring, and that further corrections to this estimate of the dimension of the diagonal coinvariant ring by ${(g+1)}^n$ should be orders of magnitude smaller. A crucial ingredient in the construction is the existence of a dot action of a certain product of symmetric groups (the Namikawa–Weyl group) acting on the parameter space of the rational Cherednik algebra and leaving invariant both the finite Hecke algebra and the spherical subalgebra; this fact is a consequence of ideas of Berest and Chalykh on the relationship between the Cherednik algebra and quasiinvariants.

对于不可约复反射群$瓦$等级$n$含有$氮$反思，我们把$G=2氮∕n$并构建一个${（G+1）}^n$Cherednik 代数的维不可约表示，它是（作为向量空间）对角协变环的商$瓦$。我们提出，切雷德尼克代数的这种表示是与对角协变环具有这种关系的单一最大表示，并且进一步修正对角协变环的维数估计：${（G+1）}^n$应该小几个数量级。构造中的一个关键因素是存在对称群（Namikawa-Weyl 群）的某种乘积的点作用，作用于有理 Cherednik 代数的参数空间，并使有限 Hecke 代数和球面子代数保持不变；这一事实是 Berest 和 Chalykh 关于 Cherednik 代数和准不变量之间关系的思想的结果。