q-discriminants and vertex operators

Discriminants and their discrete and q-analogs are usually studied in the q -analysis theory. In this paper we propose a unified realization of discrim inants using vertex operators coming from infinite dimensional Lie algebras and their quantum deformations as well as Yangian deformations. In this pi cture all of them appear as matrix coefficients of certain products of vert ex operators according to respective cases. (C) 2001 Academic Press.