Chevalley's theorem for complex crystallographic Coxeter groups
Chevalley's theorem for complex crystallographic Coxeter groups
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复杂晶体 Coxeter 群的 Chevalley 定理
DOI：
10.1007/bf01076385
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发表时间：
1978
影响因子：
0.4
通讯作者：
O. Shvartsman
中科院分区：
文献类型：
--
作者：
I. N. Bernshtein;O. Shvartsman
在Bernshtein和OV Shvartsman UDC 519.45 I中，我们考虑复晶群W，即复仿射空间V的一组离散的仿射变换，使得商X=V/W是紧的。我们假设W是由仿射反射产生的(W是ERR群)。CCR-群W称为Coxeter群(或CEC-群)，如果W的线性部分的群DW是Coxeter群(即，可以用实数矩阵在一定的基上表示)。本文的目的是刻画CCC-群W的解析空间X=V/W的结构，证明了X是一个有理簇(有奇点)，或者更准确地说，是一个“加权”射影空间。这是类似于Chvalley关于不变量的经典理论的CCC-群[I]。类似的结果显然适用于任何CCC-基团。
IN Bernshtein and OV Shvartsman UDC 519.45 i. We consider a complex crystallographic group W, ie, a discrete group of affine transformations of a complex affine space V such that the quotient X= V/W is compact. We assume that W is generated by affine reflections (W is a err-group). A ccr-group W is called a Coxeter group (or cec-group) if the group dW of linear parts of W is a Coxeter group (ie, can be expressed by real matrices in some basis). In what follows, we restrict ourselves to the case when the group W is irreducible (as an affine group).The purpose of this paper is to describe the structure of the analytic space X= V/W for a ccc-group W. It turns out that X is a rational variety (with singularities), or more precisely, a" weighted" projective space. This is an analog for ccc-groups of the classical theory of Chevalley on invariants [i]. An analogous result is apparently true for any ccc-groups.