  We study the Schur polynomial expansion of a family of symmetric polynomials
related to the refined enumeration of alternating sign matrices with respect to
their inversion number, complementary inversion number and the position of the
unique $1$ in the top row. We prove that the expansion can be expressed as a
sum over totally symmetric plane partitions and we are also able to determine
the coefficients. This establishes a new connection between alternating sign
matrices and a class of plane partitions, thereby complementing the fact that
alternating sign matrices are equinumerous with totally symmetric
self-complementary plane partitions as well as with descending plane
partitions. As a by-product we obtain an interesting map from totally symmetric
plane partitions to Dyck paths. The proof is based on a new, quite general
antisymmetrizer-to-determinant formula.
