Date of Award
1-1-2016
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
College/School/Department
Department of Mathematics and Statistics
Content Description
1 online resource (iv, 60 pages) : illustrations.
Dissertation/Thesis Chair
Cristian Lenart
Committee Members
Antun Milas, Alexandre Tchernev
Keywords
Polynomials, Lie algebras, Combinatorial analysis, Symmetry (Mathematics)
Subject Categories
Physical Sciences and Mathematics
Abstract
In 1988, Macdonald introduced two remarkable families of polynomials which bear his name. The first family is the symmetric Macdonald polynomials, which generalize the irreducible characters of semisimple Lie algebras. There are two-well known combinatorial formulas for the symmetric Macdonald polynomials — the Haglund-Haiman-Loehr formula, expressed in terms of certain tableaux but only defined in Lie type A, and the Ram-Yip formula, expressed in terms of alcove paths and defined in all Lie types. The connection between these two formulas has been established by Lenart.
Recommended Citation
Ramer, Kevin, "On combinatorial formulas for non-symmetric Macdonald polynomials" (2016). Legacy Theses & Dissertations (2009 - 2024). 1700.
https://scholarsarchive.library.albany.edu/legacy-etd/1700