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**SOME RESULTS ON GREEN'S POLYNOMIALS**

N. Sultana and Nusrat Yasmin

Centre for Advanced Studies in Pure and Applied Mathematics,

Bahauddin Zakariya University, Multan, Pakistan.

email: pdnaz@yahoo.com

** 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].

**Keywords:** Green's polynomials, partitions, Transition matrix, power sum bases.

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