  We construct nonstandard finite-dimensional representations of type C affine
Hecke algebra from the viewpoint of quantum integrable models. There exists two
classes of nonstandard solutions to the Yang-Baxter equation called the
Cremmer-Gervais and Jordanian R-matrices. These R-matrices also satisfy the
Hecke-relation, thus can be used to construct nonstandard finite-dimensional
representations of type A affine Hecke algebra. We construct the corresponding
nonstandard representations for type C affine Hecke algebra by explicitly
constructing solutions to the reflection equation under the Hecke relation. We
achieve this by taking the finite-dimensional representations and deBaxterizing
the K-operators acting on the infinite-dimensional function space, taking
advantage of the fact that the Cremmer-Gervais and Jordanian R-matrices can be
obtained from the R-operator.
