Gaussian-product unimodality conjecture

Let $n$ be a positive integer and let $k$ satisfy $0\leq k<n$. The Gaussian binomial coefficient is denoted by ${n\brack k}_q$. Consider the polynomial

$${n\brack k}_q\cdot\prod_{j=k+1}^n(1+q^j).$$

Gaussian-product unimodality conjecture. For every $0\leq k<n$, this polynomial is symmetric and unimodal. The source states that, using known results together with its preceding theorems, this formulation is equivalent to the two descent-class conjectures above. It remains open in the source.