  Alternating sign matrices with a U-turn boundary (UASMs) are a recent
generalization of ordinary alternating sign matrices. Here we show that
variations of these matrices are in bijective correspondence with certain
symplectic shifted tableaux that were recently introduced in the context of a
symplectic version of Tokuyama's deformation of Weyl's denominator formula.
This bijection yields a formula for the weighted enumeration of UASMs. In this
connection use is made of the link between UASMs and certain square ice
configuration matrices.
