Permutation statistics and \((k,\ell)\)-hook Schur functions (Q1116946)

\textit{J. Désarménien} and \textit{D. Foata} [Bull. Soc. Math. Fr. 113, 3--22 (1985; Zbl 0644.05005)] showed that many generating functions for various permutation statistics can be easily derived from classical Schur function identities and basic properties of the Robinson-Schensted correspondence. The notion of \((k,\ell)\)-hook Schur functions was introduced by \textit{A. Berele} and \textit{A. Regev} [Adv. Math. 64, 118--175 (1987; Zbl 0617.17002)] in their investigation of the representation theory of Lie subalgebras. The main purpose of the paper under review is to show that the methods of Désarménien and Foata could be extended to \((k,\ell)\)-hook Schur functions.