  An identity that is reminiscent of the Littlewood identity plays a
fundamental role in recent proofs of the facts that alternating sign triangles
are equinumerous with totally symmetric self-complementary plane partitions and
that alternating sign trapezoids are equinumerous with holey cyclically
symmetric lozenge tilings of a hexagon. We establish a bounded version of a
generalization of this identity. Further, we provide combinatorial
interpretations of both sides of the identity. The ultimate goal would be to
construct a combinatorial proof of this identity (possibly via an appropriate
variant of the Robinson-Schensted-Knuth correspondence) and its unbounded
version as this would improve the understanding of the relation between
alternating sign trapezoids and plane partition objects.
