@prefix vivo: .
@prefix edm: .
@prefix dcterms: .
@prefix dc: .
@prefix skos: .
@prefix ns0: .
vivo:departmentOrSchool "Non UBC"@en ;
edm:dataProvider "DSpace"@en ;
dcterms:creator "Frieden, Gabriel"@en ;
dcterms:issued "2019-07-23T08:21:54Z"@en, "2019-01-23T09:05"@en ;
dcterms:description """The Kostka--Foulkes polynomials, $K_{\\lambda, \\mu}(q)$, arise in many contexts in combinatorics and representation theory. Lascoux and Schutzenberger showed that they are generating functions over $\\text{SSYT}(\\lambda, \\mu)$ (the set of semistandard Young tableaux of shape $\\lambda$ and content $\\mu$) with respect to a statistic called charge. In particular, they evaluate to the familiar Kostka number at $q = 1$. One might hope that the evaluation at $q = -1$ counts the number of fixed points of a natural involution on $\\text{SSYT}(\\lambda, \\mu)$.
When the content $\\mu$ is palindromic (for instance, in the case of standard tableau) it follows from work of Stembridge and Lascoux--Leclerc--Thibon that $K_{\\lambda, \\mu}(-1)$ is equal, up to sign, to the number of elements of $\\text{SSYT}(\\lambda, \\mu)$ that are fixed by evacuation (the Schutzenberger involution). This restriction on $\\mu$ is necessary because evacuation is content-reversing.
In recent joint work with Mike Chmutov, Dongkwan Kim, Joel Lewis, and Elena Yudovina, we showed that in general, $K_{\\lambda, \\mu}(-1)$ counts, up to sign, the number of fixed points of the involution obtained by composing evacuation with the action of the long element $w_0$ by the Lascoux--Schutzenberger (or crystal) symmetric group action on tableaux. When the content is palindromic, the action of $w_0$ is trivial, so our result reduces to the above-mentioned one. The proof relies on the theory of rigged configurations."""@en ;
edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/71069?expand=metadata"@en ;
dcterms:extent "49.0"@en ;
dc:format "video/mp4"@en ;
skos:note ""@en, "Author affiliation: Université du Québec à Montréal"@en ;
dcterms:spatial "Banff (Alta.)"@en ;
edm:isShownAt "10.14288/1.0379941"@en ;
dcterms:language "eng"@en ;
ns0:peerReviewStatus "Unreviewed"@en ;
edm:provider "Vancouver : University of British Columbia Library"@en ;
dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ;
dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ;
ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ;
ns0:scholarLevel "Postdoctoral"@en ;
dcterms:isPartOf "BIRS Workshop Lecture Videos (Banff, Alta)"@en ;
dcterms:subject "Mathematics"@en, "Group theory and generalizations"@en, "Combinatorics"@en ;
dcterms:title "Kostka--Foulkes polynomials at $q = -1$"@en ;
dcterms:type "Moving Image"@en ;
ns0:identifierURI "http://hdl.handle.net/2429/71069"@en .