G-簇的拟周期填充与Baake-Moody集
Quasiperiodic packings of G-clusters and Baake-Moody sets
摘要：
准晶的衍射图样允许有限群G作为对称群，并且存在G-簇C（G的轨道的并集），使得准晶可以被视为C的副本的准周期堆积，通常，部分占据。另一方面，通过从G-簇C出发，我们可以在高维空间中以规范的方式定义G的置换表示，将该空间分解为两个G-不变子空间的正交和，并使用条带投影方法来定义一种模式，该模式也可以被视为C的副本的准周期包装，通常，部分占用。这种数学算法在准晶物理中是有用的，但是在两壳层或三壳层团簇的情况下，我们必须使用的超空间的维数相当大。我们表明，由Baake和Moody [Proc. Int. Conf. Aperiodic' 97（Alpe d' Huez，1997年8月27-31日）ed M de Boissieu et al.（Singapore：World Scientific，1999）pp 9-20]提出的关于条带投影方法的推广允许降低该维度，并给出了一些例子。
英文摘要：
The diffraction pattern of a quasicrystal admits as symmetry group a finite group G, and there exists a G-cluster C (a union of orbits of G) such that the quasicrystal can be regarded as a quasiperiodic packing of copies of C, generally, partially occupied. On the other hand, by starting from the G-cluster C we can define in a canonical way a permutation representation of G in a higher dimensional space, decompose this space into the orthogonal sum of two G-invariant subspaces and use the strip projection method in order to define a pattern which can also be regarded as a quasiperiodic packing of copies of C, generally, partially occupied. This mathematical algorithm is useful in quasicrystal physics, but the dimension of the superspace we have to use in the case of a two or three-shell cluster is rather large. We show that the generalization concerning the strip projection method proposed by Baake and Moody [Proc. Int. Conf. Aperiodic' 97 (Alpe d'Huez, 27-31 August, 1997) ed M de Boissieu et al. (Singapore: World Scientific, 1999) pp 9-20] allows to reduce this dimension, and present some examples.
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