A geometric version of the Robinson–Schensted correspondence for skew oscillating tableaux

AbstractWe consider an analogue of the Robinson–Schensted correspondence for skew oscillating tableaux and we propose a geometric version of this correspondence, extending similar constructions for standard (Combinatoire et représentation du groupe symétrique, Lecture Notes in Mathematics, Vol. 579, Springer, Berlin, 1977, pp. 29–58) and oscillating tableaux (Formal Power Series and Algebraic Combinatorics, FPSAC’99, Univ. Politecnicà de Catalunya, 1999, pp. 141–152). We deduce from this geometric construction new proofs of some combinatorial properties of this correspondence