  We study certain non-symmetric wavefunctions associated to the quantum
nonlinear Schr\"odinger (QNLS) model, introduced by Komori and Hikami using
representations of the degenerate affine Hecke algebra. In particular, they can
be generated using a vertex operator formalism analogous to the recursion that
defines the symmetric QNLS wavefunction in the quantum inverse scattering
method. Furthermore, some of the commutation relations encoded in the
Yang-Baxter equation are generalized to the non-symmetric case.
