  We prove and conjecture some new symmetric function identities, which equate
the generating series of 1. Plane partitions, subject to certain restrictions
and weightings, and 2. Alternating sign matrices, subject to certain symmetry
properties. The left hand side of each of our identities is a simple refinement
of a relevant Cauchy or Littlewood identity, allowing them to be interpreted as
generating series for plane partitions. The right hand side of each identity is
a partition function of the six-vertex model, on a relevant domain. These can
be interpreted as generating series for alternating sign matrices, using the
well known bijection with six-vertex model configurations.
