"Non UBC"@en .
"DSpace"@en .
"Frieden, Gabriel"@en .
"2019-07-23T08:21:54Z"@en .
"2019-01-23T09:05"@en .
"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."@en .
"https://circle.library.ubc.ca/rest/handle/2429/71069?expand=metadata"@en .
"49.0"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Universit\u00E9 du Qu\u00E9bec \u00E0 Montr\u00E9al"@en .
"Banff (Alta.)"@en .
"10.14288/1.0379941"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Postdoctoral"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Group theory and generalizations"@en .
"Combinatorics"@en .
"Kostka--Foulkes polynomials at $q = -1$"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/71069"@en .