The spectrum of the transfer matrices connected with Kac-Moody algebras

The spectrum of the transfer matrices corresponding to trigonometrical Bazhanov-Jimbo R matrices is found. The Bethe equations characterizing the eigenvalues of the transfer matrices are written down in terms of root systems. Using the generalization of the Bethe equations for Kac-Moody algebras D_inf4^sup(3), G_inf2^sup(1), E_inf6^sup(1)and E_inf6^sup(2), we give conjectures for the eigenvalues of the corresponding transfer matrices.