Abstract
Previous results for the generation of linear, icosahedral, Jahn-Teller (JT) Hamiltonians with continuous group symmetries are extended. It is demonstrated that it is possible to define electronic generalized tensor operators on a direct sum electronic space such that a set of these operators is closed under commutation with another set of electronic generalized tensor operators which act as the generators of a continuous group. The normal modes carrying irreducible representations of the continuous group are then coupled `equally' to produce a JT Hamiltonian which is invariant under the operations of the continuous group. The continuous groups generated on the direct sum spaces 
, 
, 
and 
are discussed in detail. These additional continuous groups are of interest when the lowest JT states of certain icosahedral JT systems (such as some of those found in 
) are modelled. The additional continuous group symmetry allows an analytic diagonalization of the linear JT matrix to be provided and thus facilitates an exact treatment of the vibronic ground state for these models.