Partially-Symmetric Macdonald Polynomials
| dc.contributor.author | Goodberry, Benjamin Nathaniel | en |
| dc.contributor.committeechair | Orr, Daniel D. | en |
| dc.contributor.committeemember | Mihalcea, Constantin Leonardo | en |
| dc.contributor.committeemember | Shimozono, Mark M. | en |
| dc.contributor.committeemember | Loehr, Nicholas A. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2022-03-30T08:00:13Z | en |
| dc.date.available | 2022-03-30T08:00:13Z | en |
| dc.date.issued | 2022-03-29 | en |
| dc.description.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. 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. | en |
| dc.description.abstractgeneral | 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. | en |
| dc.description.degree | Doctor of Philosophy | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:34181 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/109496 | en |
| dc.language.iso | en | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | Macdonald theory | en |
| dc.subject | Partially Symmetric | en |
| dc.subject | Almost Symmetric | en |
| dc.title | Partially-Symmetric Macdonald Polynomials | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |
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