Non UBC
DSpace
Assaf, Sami
2019-07-22T09:12:13Z
2019-01-22T14:02
Nonsymmetric Macdonald polynomials are a polynomial generalization of their symmetric counterparts that exist for all root systems. The combinatorial formula for type A, due to Haglund, Haiman and Loehr, resembles the symmetric formula by the same authors, but with rational functions that complicate the combinatorics. By specializing one parameter to 0, the combinatorics simplifies and we are able to give an explicit formula for the expansion into Demazure characters, a basis for the polynomial ring that contains and generalizes the Schur basis for symmetric polynomials. The formula comes via an explicit Demazure crystal structure on semistandard key tabloids, constructed jointly with Nicolle Gonzalez. By taking stable limits, we return to the symmetric setting and obtain a new formula for the Schur expansion of Hall-Littlewood polynomials that uses a simple major index statistic computed from highest weights of the crystal.
https://circle.library.ubc.ca/rest/handle/2429/71067?expand=metadata
60.0
video/mp4
Author affiliation: University of Southern California
Banff (Alta.)
10.14288/1.0379936
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Group theory and generalizations
Combinatorics
Nonsymmetric Macdonald polynomials and Demazure characters
Moving Image
http://hdl.handle.net/2429/71067