Proof of Two Multivariate q-Binomial Sums Arising in Gromov-Witten Theory
Abstract
We prove two multivariate q-binomial identities conjectured by Bousseau, Brini and van Garrel [Geom. Topol. 28 (2024), 393-496, arXiv:2011.08830] which give generating series for Gromov-Witten invariants of two specific log Calabi-Yau surfaces. The key identity in all the proofs is Jackson's q-analogue of the Pfaff-Saalsch\"utz summation formula from the theory of basic hypergeometric series.
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