Por Inês Martins Rodrigues (aluna de doutoramento da FCUL).

Abstract: The Robinson-Schensted correspondence, introduced by Schensted (1961) in its most well-known form, presents a bijective correspondence between permutations and pairs of standard Young tableaux of the same shape. Knuth (1970) presented a generalization, the RSK correspondence, for semistandard Young tableaux.

As the Young tableaux are deeply tied to the study of linear representations of the symmetric group, there is a variant for the projective representations, the shifted tableaux, based on strict partitions. The shifted tableaux also arise in the study of Q-functions, an important basis for the subalgebra of the symmetric functions generated by the odd power sums, which resembles the classic Schur functions.

In this seminar, we will show generalizations of both Robinson-Schensted and RSK correspondences for skew tableaux and analogues for shifted skew tableaux (Sagan, Stanley, 1990), based on variants of the insertion algorithm. We will also present a brief introduction on some aspects of the theory of shifted tableaux.