Nested ansatz method for Baker-Akhiezer functions

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 [A. Mironov, A. Morozov, and A. Popolitov, ] but for the generally nonsymmetric BAF. We demonstrate that, for usual nontwisted ( a = 1 ) BAFs, this method correctly reproduces the Noumi-Shiraishi formula directly from linear equations, resolving the ambiguity related to nonsimple roots. For the first nontrivial 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 of the above article.