{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/109496"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/109496","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Partially-Symmetric Macdonald Polynomials","abstract":"Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald polynomials interpolate between the symmetric and nonsymmetric types. 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We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald polynomials interpolate between the symmetric and nonsymmetric types. We begin developing theory for these partially-symmetric polynomials, and prove results including their stability, an integral form, and a Pieri-like formula for their multiplication with certain elementary symmetric functions."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["There are two well-understood types of polynomials known as the nonsymmetric Macdonald polynomials and symmetric Macdonald polynomials. We define a new form of Macdonald polynomials, which we call partially-symmetric, that are somewhere between the symmetric and nonsymmetric versions. We examine properties of these new partially-symmetric polynomials, including what happens when adding additional symmetric variables, how to multiply them by a constant to clear out denominators in their coefficients, and what happens when multiplying them by another symmetric polynomial."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Partially-Symmetric Macdonald Polynomials"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Orr, Daniel D."],"dc:contributor.committeemember":["Mihalcea, Constantin Leonardo","Shimozono, Mark M.","Loehr, Nicholas A."],"dc:contributor.department":["Mathematics"],"dc:creator":["Goodberry, Benjamin Nathaniel"],"dc:date.accessioned":["2022-03-30T08:00:13Z"],"dc:date.available":["2022-03-30T08:00:13Z"],"dc:date.issued":["2022-03-29"],"dc:description.abstract":["Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. 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