| Summary: | Theories of symmetry-based indicators and topological quantum chemistry, while powerful in diagnosing gapped topological materials, cannot be directly applied to diagnosing band degeneracies at/between high-symmetry momenta due to the violation of the compatibility conditions. However, the only information that compatibility condition can tell us is whether there are band degeneracies at/between high-symmetry momenta or not. Here we design a recursive protocol that utilizes indicators of maximal subgroups to infer the topological information of band degeneracies crossing high-symmetry lines without implementing a heavy numerical calculation, such as the existence, type, number, configuration for the band degeneracies, and so on. For demonstration, the method is used to predict the existence of ideal Weyl phonons in In_{2}Te and node-cage phonons in ZrSiO, respectively.
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