Hook flag characters and their combinatorics
These are the characters \(\chi(a;b)\) of the representations of \(S_ n\) induced by the representations \([a_ 1]\#...\#[a_ k]\#[1^{b_ 1}]\#...\#[1^{b_ l}]\) of the subgroups \(S(a;b):=S_{a_ 1}\times...\times S_{a_ k}\times S_{b_ 1}\times,..\times S_{b_ l}\) (natural embedding), were \(\sum a_ i+\sum b_ j=n\). Continuing earlier research [(to appear in) Adv. Math. 64, 118--175 (1987; Zbl 0617.17002)] the authors decompose \(\chi(a;b)\otimes\chi(c;d)\) and give a construction analogous to the Schensted-Knuth correspondence adapted to so-called \((k,l)\)-semistandard tableaux which are needed here.
scientific article; zbMATH DE number 3871621
scientific article