Canonical bases and self-evacuating tableaux
This article is centered around the problem of enumerating semi-standard and standard tableaux fixed by an involution defined by Schützenberger and called ``evacuation''. The author obtains several representation theoretic expressions for these numbers. For this he first gives an expression in representation theoretic terms for the number of fixed points of Lusztig's involution on the canonical basis of an irreducible finite dimensional representation. By work of \textit{A. Berenstein} and \textit{A. Zelevinsky} [Duke Math. J. 82, 473-502 (1996)] Lusztig's involution corresponds in type \(A\) to Schützenberger's under a suitable parametrization of the canonical basis by semi-standard tableaux. This then leads to the main results.
scientific article; zbMATH DE number 908702
scientific article