A given JT problem will have a particular point group symmetry, such as T symmetry for magnetic impurity ions in semiconductors or I symmetry for the fullerene C. JT problems are conventionally classified using labels for the irreducible representations (irreps) that apply to the symmetry of the electronic and vibrational states. For example, E ⊗ e would refer to an electronic doublet state transforming as E coupled to a vibrational doublet state transforming as e.
In general, a vibrational mode transforming as Λ will couple to an electronic state transforming as Γ if the symmetric part of the Kronecker product [Γ ⊗ Γ] contains Λ, unless Γ is a double group representation when the antisymmetric part {Γ ⊗ Γ} is considered instead. Modes which do couple are said to be JT-active.
As an example, consider a doublet electronic state E in cubic symmetry. The symmetric part of E ⊗ E is A + E. Therefore, the state E will couple to vibrational modes  transforming as a and e. However, the a modes will result in the same energy shift to all states and therefore do not contribute to any JT splitting. They can therefore be neglected. The result is an E ⊗ e JT effect. This JT effect is experienced by triangular molecules X, tetrahedral molecules ML, and octahedral molecules ML when their electronic state has E symmetry.
Components of a given vibrational mode are also labelled according to their transformation properties. For example, the two components of an e mode are usually labelled  and , which in octahedral symmetry transform as  and  respectively.