{"http:\/\/dx.doi.org\/10.14288\/1.0379941":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Non UBC","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Frieden, Gabriel","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2019-07-23T08:21:54Z","type":"literal","lang":"en"},{"value":"2019-01-23T09:05","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"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 $\\text{SSYT}(\\lambda, \\mu)$.\n\nWhen 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.\n\nIn 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.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/71069?expand=metadata","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/extent":[{"value":"49.0","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/elements\/1.1\/format":[{"value":"video\/mp4","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"","type":"literal","lang":"en"},{"value":"Author affiliation: Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/spatial":[{"value":"Banff (Alta.)","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt":[{"value":"10.14288\/1.0379941","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/language":[{"value":"eng","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#peerReviewStatus":[{"value":"Unreviewed","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/provider":[{"value":"Vancouver : University of British Columbia Library","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/publisher":[{"value":"Banff International Research Station for Mathematical Innovation and Discovery","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/rights":[{"value":"Attribution-NonCommercial-NoDerivatives 4.0 International","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#rightsURI":[{"value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#scholarLevel":[{"value":"Postdoctoral","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/isPartOf":[{"value":"BIRS Workshop Lecture Videos (Banff, Alta)","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/subject":[{"value":"Mathematics","type":"literal","lang":"en"},{"value":"Group theory and generalizations","type":"literal","lang":"en"},{"value":"Combinatorics","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/title":[{"value":"Kostka--Foulkes polynomials at $q = -1$","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/type":[{"value":"Moving Image","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#identifierURI":[{"value":"http:\/\/hdl.handle.net\/2429\/71069","type":"literal","lang":"en"}]}}