Mason’s question for second symmetric powers of uniform matroids

Determine whether, for all n and t, the family of second symmetric powers of the uniform matroid U^t_n has a unique maximal element under the weak order (and, if so, identify it).

Background

For linear representations over characteristic 0, one canonical second symmetric power arises from symmetric tensors, and for R_d this matroid is dual to the rigidity matroid when t = n−1−d. The paper proves that the generic second symmetric power is not always maximal (t ≥ 7), leaving the existence of a unique maximal element open.

Resolving this question would generalize maximality phenomena from rigidity to symmetric-tensor matroids.