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Hybrid pipe dreams for the lower-upper scheme
Allen Knutson, Paul Zinn-Justin
https://arxiv.org/abs/2509.01857 https://arxiv.org/pdf/2509.01857

Hybrid pipe dreams for the lower-upper scheme
In [KU23] were introduced hybrid pipe dreams interpolating between classic and bumpless pipe dreams, each hybridization giving a different formula for double Schubert polynomials. A bijective proof was given (following [GH23]) of the independence of hybridization, but only for nonequivariant Schubert polynomials. In this paper we further generalize to hybrid generic pipe dreams, replacing the bijective proof of hybridization-independence with a Yang-Baxter-based proof that allows one to maintai…