Hall–Littlewood P-positivity of q-divided symmetrized Schubert polynomials

Let $cmathfrak{S}_{w}(x_1,\cdots,x_n)$ be a Schubert polynomial, and let $clangle cmathfrak{S}_{w}crangle_n^q$ denote its $q$-divided symmetrization. A symmetric polynomial is Hall–Littlewood P-positive if it is a nonnegative linear combination of Hall–Littlewood $P$-polynomials. Hall–Littlewood P-positivity conjecture. The polynomial $clangle cmathfrak{S}_{w}crangle_n^q$ is Hall–Littlewood P-positive. This conjecture extends the known coefficientwise nonnegativity of ordinary divided symmetrizations and predicts a stronger positivity property for the $q$-analogue; the source reports that it arose from computer experimentation.