Increasing attention is being focused on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed, significant difficulties can arise such as the generation of too many or too few basis functions to minimally span the linear vector space. We present an elegant solution to these difficulties using the concept of basis sets and discuss previous work in this area using this concept. Further, we highlight the significance of unitary irreducible representations in this method and provide the first validation that the irreducible representations of the crystallographic space groups tabulated by Kovalev are unitary.

中文翻译：

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生成磁性结构和位移模式的基向量

越来越多的注意力集中在使用对称适应函数来描述磁结构、结构畸变和不协调的晶体学上。尽管此类函数的计算得到了很好的发展，但可能会出现重大困难，例如生成过多或过少的基函数以最小化线性向量空间。我们使用基组的概念为这些困难提供了一个优雅的解决方案，并使用这个概念讨论了该领域以前的工作。此外，我们强调了该方法中酉不可约表示的重要性，并首次验证了 Kovalev 列出的晶体空间群的不可约表示是酉表示。