2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69629A characterization of the space of symmetric Laurent polynomials of type $(BC)_n$ which vanish on a certain set of submanifolds is given by using the Koornwinder-Macdonald polynomials. A similar characterization was given previously for symmetric polynomials of type $A_n$ by using the Macdonald polynomials. We use a new method which exploits the duality relation. The method simplifies a part of the proof in the $A_n$ case.15 pages, self-duality condition is not necessary, so it is removedQuantum AlgebraCombinatoricstext