  An analysis of the Kimura 3ST model of DNA sequence evolution is given on the
basis of its continuous Lie symmetries. The rate matrix commutes with a
U(1)xU(1)xU(1) phase subgroup of the group GL(4) of 4x4x4 invertible complex
matrices acting on a linear space spanned by the 4 nucleic acid base letters.
The diagonal `branching operator' representing speciation is defined, and shown
to intertwine the U(1)xU(1)xU(1) action. Using the intertwining property, a
general formula for the probability density on the leaves of a binary tree
under the Kimura model is derived, which is shown to be equivalent to
established phylogenetic spectral transform methods.
