Abstract We construct novel families of exact immersed and embedded Lagrangian translating solitons and special Lagrangian submanifolds in Cᵐ C m that are invariant under the action of various admissible compact subgroups G {\, SU\, } (m-1) G ≤ SU (m - 1) with cohomogeneity-two. These examples are obtained via an Ansatz generalising a construction of Castro–Lerma in C² C 2. We give explicit examples of admissible group actions, including a full classification for G simple. We also describe novel Lagrangian translators symmetric with respect to non-compact subgroups of the affine special unitary group {\, SU\, } (m) Cᵐ SU (m) ⋉ C m, including cohomogeneity-one examples.
Su et al. (Wed,) studied this question.