|
|
| Schensted insertion algorithm for Young tableaux provides a
combinatorial rule for computing Littlewood-Richardson coefficients
(structure constants of grassmannians). We discuss modifications of this
algorithm which work with rc-graphs instead of Young tableaux and provide
rules for computing generalized Littlewood-Richardson coefficients
(structure constants of flag manifolds). The latest version of the
algorithm computes the coefficients $c^u_{wv}$ in the cases when v
is a grassmannian permutation, whose shape is a hook, or in the case
when v is a grassmannian permutation with the single descent at $k$ and w
is a permutation with no descents greater than $k$. The algorithm also
allows to generalize the RSK correspondence in these cases.
|
|