A Simple Proof of an Aomoto-Type Extension of Askey’s Last Conjectured Selberg q-Integral

We establish an Aomoto-type extension of Askey’s last conjectured Selberg q-integral, which was recently proved by Evans. We follow the lines of our proofs of Aomoto-type extensions of the Morris constant term q-identity and Gustafson’s Askey–Wilson Selberg q-integral. We require integral forms of the q-transportation theory and its alternative for the root system An−1, which are related to the simple reflections and minuscule weight of An−1. We use an elementary symmetry which is related to the minuscule weight of An−1 to lift a proof of the one dimensional q-integral to the multivariable setting.