Review of Symmetry and Representations in Band Theory

Crystalline symmetries, such as lattice translations and rotations, play a pivotal role in studies on both superconductivity and topological phases. In this chapter, we review representation theory in band structures and the original symmetry-indicator theory. Although we focus only on normal phases here, most notions introduced in this chapter are common to superconducting phases. In fact, we will use them to introduce representation theory for superconducting phases in the next chapter. Furthermore, the review of symmetry-indicator theory for normal conducting phases would clarify the difference in the theory for superconducting phases, which is discussed in Chap. 3.