For a class of one-dimensional reaction-diffusion equations, we establish the existence of generalized fronts, as recently defined by Berestycki and Hamel. We also prove uniform nondegeneracy estimates, such as a lower bound on the time derivative on some level sets, as well as a lower bound on the spatial derivative.

Tokuyama [31] proved a deformation of the Weyl character formula for GL (C). A substantial generalization of Tokuyama's deformation was found by Hamel and King [8]. The formula of Hamel and King expresses the Schur polynomial times a deformation of the Weyl denominator as a sum over states of the two-dimensional ice or six-vertex model in statistical mechanics. It turns out that there are two f...