Robinson-Schensted-type algorithms for the spinor representations of the orthogonal Lie algebra \({\mathfrak so}(2n,\mathbb{C})\)
The ordinary representation theory of the classical linear groups, arising from the intertwining action of appropriate symmetric groups, devolves on the manipulation of Young diagrams and Young tableaux. There is an extension of spinor representations which requires the addition of half boxes to the usual diagrams. Furthermore, there is a subset of the set of all tableaux, called semi-standard tableaux, in which the tableaux entries are strictly increasing down columns but weakly increasing along rows. In this paper the author extends the so-called Robinson-Schensted algorithm for the manipulation of semi-standard tableaux, which may be used to reduce certain representations, to encompass the spinor representations of the orthogonal algebra \({\mathfrak {so}}( 2n,\mathbb{C})\).
scientific article; zbMATH DE number 218575