Stokes Harold T, Campbell Branton J, Cordes Ryan
Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA.
Acta Crystallogr A. 2013 Jul;69(Pt 4):388-95. doi: 10.1107/S0108767313007538. Epub 2013 May 8.
New tables of irreducible representations (IRs) are introduced for the 230 crystallographic space groups (SGs) in three-dimensional space, at both special and non-special k vectors, and for their extensions to (3 + d)-dimensional superspace (`superspace-extended SGs' or SSESGs). Neither a tabulation of SG IR matrices for non-special k vectors nor a tabulation of SSESG IR matrices for d > 1 have been previously published. These tabulations are made possible by a new form in which the IR matrices of SGs are separated as a product of a translation part T and a point-operation part P, and where the IR matrices of SSESGs are separated as a product of a phase-shift part Q and a point-operation part P(s). Both T and Q have a simple prescribed form that does not need to be tabulated. Also, the new IR matrices are in a convenient block form which allows one to see by inspection which parts of the matrices and the associated order parameters belong to which arm of the star of k. In addition to complex IR matrices, real physically irreducible representation (PIR) matrices are tabulated. The new IR and PIR tables are available on the ISO-IR website (http://stokes.byu.edu/iso/irtables.php) in both convenient human-readable and computer-readable forms.
本文引入了三维空间中230个晶体学空间群（SGs）在特殊和非特殊k矢量处的不可约表示（IRs）新表，以及它们到（3 + d）维超空间（“超空间扩展SGs”或SSESGs）的扩展。此前尚未发表过非特殊k矢量的SG IR矩阵表，也未发表过d > 1的SSESG IR矩阵表。这些表的实现得益于一种新形式，其中SGs的IR矩阵被分离为平移部分T和点操作部分P的乘积，而SSESGs的IR矩阵被分离为相移部分Q和点操作部分P(s)的乘积。T和Q都具有简单的规定形式，无需列表。此外，新的IR矩阵采用了方便的分块形式，通过检查可以看出矩阵的哪些部分以及相关的序参量属于k星的哪一支。除了复IR矩阵外，还列出了实物理不可约表示（PIR）矩阵。新的IR和PIR表可在ISO-IR网站（http://stokes.byu.edu/iso/irtables.php）上以方便人类阅读和计算机可读的形式获取。
