Goodberry, Benjamin Nathaniel2018-06-202018-06-202018-06-19vt_gsexam:15656http://hdl.handle.net/10919/83576The Kostka-Foulkes polynomials describe the change of basis between Schur polynomials and Hall-Littlewood polynomials. In this paper, we extend this idea to the family of BCn Macdonald spherical functions, with multiparameter Kostka-Foulkes polynomials acting as the change of basis from the BC_n spherical functions to the type Cn Schur polynomials. We develop a Kato-Lusztig formula that describes the multiparameter BCn-Kostka-Foulkes polynomials.ETDIn CopyrightHall-Littlewood PolynomialsKostka-Foulkes PolynomialsAlgebraic CombinatoricsThesis