Nested ansatz method for Baker-Akhiezer functions
Abstract
We explain that the logic behind the derivation of the Noumi-Shiraishi function can be applied directly to the Baker-Akhiezer function (BAF). This amounts to changing an ansatz for BAF to a nested one, where the BAF of N + 1 variables is recursively expressed as a sum over BAFs of N variables. This may be seen as a generalization of symmetrization trick from [1], but for the generally non-symmetric BAF. We demonstrate that, for usual non-twisted (a = 1) BAFs, this method correctly reproduces the Noumi-Shiraishi formula directly from linear equations, resolving the ambiguity related to non-simple roots. For the first non-trivial twisted case (N = 3, a = 2) this method also fixes this ambiguity, moreover, answers for the first few layers of coefficients are in the form of direct quantization of [1].
Cite
@article{arxiv.2601.17453,
title = {Nested ansatz method for Baker-Akhiezer functions},
author = {A. Mironov and A. Morozov and A. Popolitov},
journal= {arXiv preprint arXiv:2601.17453},
year = {2026}
}