The inversion relation and the dilute A_{3,4,6} eigenspectrum
  On the basis of the result obtained by applying Baxter's exact perturbative approach to the dilute A_3 model to give the E_8 mass spectrum, the dilute A_L inversion relation was used to predict the eigenspectra in the L=4 and L=6 cases (corresponding to E_7 and E_6 respectively). In calculating the next-to-leading term in the correlation lengths, or equivalently masses, the inversion relation condition gives a surprisingly simple result in all three cases, and for all masses. 
Katherine A Seaton (La Trobe) and M. T. Batchelor (ANU)