An occurrence of the Robinson-Schensted correspondence
Let \({\mathcal F}\) be the flag manifold of an \(n\)-dimensional vector space \(V\). To each unipotent transformation \(u\) of \(V\), denote by \({\mathcal F}_ u\) the variety of flags fixed by \(u\). In this paper it is shown that the element of \(S_ n\) which determines the relative position of two irreducible components is equal to the element given by the Robinson-Schensted correspondence applied to the associated two standard tableaux. As pointed out by the author a proof of this result has also been given by \textit{N. Spaltenstein} [in: Classes unipotentes et sous groupes de Borel. Lect. Notes Math. 946. Berlin etc.: Springer Verlag (1982; Zbl 0486.20025)] although the Robinson-Schensted process is there only implicit.
scientific article; zbMATH DE number 4065283