Multiparameter BCn-Kostka-Foulkes Polynomials

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dc.contributor.authorGoodberry, Benjamin Nathanielen
dc.contributor.committeechairOrr, Daniel D.en
dc.contributor.committeememberLoehr, Nicholas A.en
dc.contributor.committeememberShimozono, Mark M.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2018-06-20T08:02:42Zen
dc.date.available2018-06-20T08:02:42Zen
dc.date.issued2018-06-19en
dc.description.abstractThe 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.en
dc.description.abstractgeneralThe work done in [11] gives a formula to calculate Kostka-Foulkes polynomials that convert between two other forms of polynomials. However, this only applies in specific instances. In this paper, we generalize those ideas to allow for more parameters, and find that a similar formula still holds.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:15656en
dc.identifier.urihttp://hdl.handle.net/10919/83576en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectHall-Littlewood Polynomialsen
dc.subjectKostka-Foulkes Polynomialsen
dc.subjectAlgebraic Combinatoricsen
dc.titleMultiparameter BCn-Kostka-Foulkes Polynomialsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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