Bispectrality and the ad conditions
Mathematical Physics
2026-05-15 v2 math.MP
Abstract
At the beginning of the study of the bispectral problem, see [18], the ad-conditions played a crucial role in finding non-classical instances. The connection with the ad-conditions has reappeared in several different incarnations of the bispectral problem. Here we show that, properly adapted versions of these conditions, see [44], can play an important role in areas including, for instance, the study of exceptional orthogonal polynomials. This is also true in the non-commutative case. Even at this more advanced stage of the field one may hope that finding explicit solutions of these ad-conditions will provide an additional route to new examples.
Cite
@article{arxiv.2603.00939,
title = {Bispectrality and the ad conditions},
author = {F. Alberto Grunbaum},
journal= {arXiv preprint arXiv:2603.00939},
year = {2026}
}