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I am writing calculation software for computing structure constants of equivariant quantum Schubert polynomials and I discovered that partial flag varieties corresponding to parabolic subgroups have different polynomials (fleshed out, for example, in section 6.2 in this paper).

All I need to do the computation is a Pieri formula for multiplying by a parabolic quantum elementary polynomial. An equivariant Pieri formula is likely not available (and wouldn't be sufficient anyway, I would need a Pieri formula for multiplying in different sets of variables), but is there at least a known Pieri formula for ordinary parabolic quantum Schubert polynomials? I was unable to find anything but maybe my searching abilities are lacking.

I'm aware of the Chevalley formula, and technically that's sufficient, but it would be super slow to implement it that way.

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An answer to this is essentially given by Postnikov's Pieri formula for quantum Schubert polynomials combined with the Peterson-Woodward comparison formula.

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