SpaceGroupIrep swMATH ID: 36355 Software Authors: Liu, Gui-Bin; Chu, Miao; Zhang, Zeying; Yu, Zhi-Ming; Yao, Yugui Description: SpaceGroupIrep: A package for irreducible representations of space group. We have developed a Mathematica program package SpaceGroupIrep which is a database and tool set for irreducible representations (IRs) of space group in BC convention, i.e. the convention used in the famous book ”The mathematical theory of symmetry in solids” by C. J. Bradley & A. P. Cracknell. Using this package, elements of any space group, little group, Herring little group, or central extension of little co-group can be easily obtained. This package can give not only little-group (LG) IRs for any k-point but also space-group (SG) IRs for any k-stars in intuitive table form, and both single-valued and double-valued IRs are supported. This package can calculate the decomposition of the direct product of SG IRs for any two k-stars. This package can determine the LG IRs of Bloch states in energy bands in BC convention and this works for any input primitive cell thanks to its ability to convert any input cell to a cell in BC convention. This package can also provide the correspondence of k-points and LG IR labels between BCS (Bilbao Crystallographic Server) and BC conventions. In a word, the package SpaceGroupIrep is very useful for both study and research, e.g. for analyzing band topology or determining selection rules. Homepage: https://arxiv.org/abs/2012.08871 Source Code: https://github.com/goodluck1982/SpaceGroupIrep Dependencies: Mathematica Keywords: Materials Science; arXiv_cond-mat.mtrl-sci; Computational Physics; arXiv_physics.comp-ph; Mathematica; irreducible representations; space group; little group; direct product Related Software: ISOTROPY; Mathematica; ABINIT; Quantum Espresso; Bilbao Crystallography Server; MSGCorep; NanoNET; Qsymm; MagneticTB; PythTB; Z2pack; Kwant; Wannier90; VASP; Spglib; WIEN2k; GAP; MagneticKP; SPRKKR; Tight-Binding Studio Cited in: 5 Documents Standard Articles 2 Publications describing the Software, including 1 Publication in zbMATH Year SpaceGroupIrep: a package for irreducible representations of space group. Zbl 1523.85001Liu, Gui-Bin; Chu, Miao; Zhang, Zeying; Yu, Zhi-Ming; Yao, Yugui 2021 SpaceGroupIrep: A package for irreducible representations of space group arXiv Gui-Bin Liu, Miao Chu, Zeying Zhang, Zhi-Ming Yu, Yugui Yao 2020 all top 5 Cited by 9 Authors 4 Liu, Gui-Bin 4 Yao, Yugui 4 Yu, Zhi-Ming 4 Zhang, Zeyin 1 Bradley, Christopher J. 1 Chu, Miao 1 Cracknell, Arthur P. 1 Li, Zhenye 1 Yang, Shengyuan A. Cited in 1 Serial 4 Computer Physics Communications all top 5 Cited in 11 Fields 4 Group theory and generalizations (20-XX) 4 Statistical mechanics, structure of matter (82-XX) 2 Quantum theory (81-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Geometry (51-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year