VERTEX OPERATORS AND HALL-LITTLEWOOD SYMMETRICAL FUNCTIONS

We consider vertex operators on space V with a parameter t. Their components form an associative algebra which is a generalization of the Clifford algebra. A distinguished orthogonal basis of V is proved to be the Hall-Littlewood symmetric functions. We show that Kostka-Foulkes polynomials (or certain Kazhdan-Lusztig polynomials for the affine Weyl group of type A) are matrix coefficients on the space V. We also obtain certain generating functions for the product of Hall-Littlewood functions and the Kostka-Foulkes polynomials. © 1991.