SOME RESULTS ON GREEN’S POLYNOMIALS

Abstract

The transition matrix X(t) between the power sum product and Hall-Littlewood function gives us Green’s polynomials. These polynomials are useful in the construction of the irreducible characters of GL(n, q), see [Green 1955] and [Morris 1963]. In this paper we consider the special case t = w, where w is a primitive pth root of unity. Our intension is to give proof of some conjectures [Morris and Sultana 1991].