Partially-Symmetric Macdonald Polynomials

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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2022

Author dc:creator

• Goodberry, Benjamin Nathaniel

Chair dc:contributor.committeechair

• Orr, Daniel D.

Committee members dc:contributor.committeemember

• Mihalcea, Constantin Leonardo
• Shimozono, Mark M.
• Loehr, Nicholas A.

• Macdonald theory
• Partially Symmetric
• Almost Symmetric

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:34181

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/109496