Consider the cohomology ring of the Grassmannian of k-planes in complex n-space. It has a standard presentation as a quotient of the ring of symmetric functions. In this presentation, the Schur functions are mapped to the Schubert classes, thus have a nice geometric interpretation.


One can generalise the Schur functions to skew-Schur functions. Do these also have a nice geometric interpretation?



Is there a geometric interpretation of skew Schur functions?
This is discussed in Stanley's paper *Some combinatorial aspects of the Schubert calculus*. Corollary 3.7 says that under the natural isomorphism given by the Borel presentation of $H^\*(G/P)$ which sends an ordinary Schur function $s\_{\lambda}$ to the class of the Schubert variety $X\_{\lambda}$, a skew Schur function $s\_{\lambda / \mu}$ is sent to the class of the Richardson variety $X\_{\lambda}^{\mu}$.


Note that Stanley calls Richardson varieties *skew Schubert varieties* in this paper. Unfortunately, the [version of the paper](http://www-math.mit.edu/~rstan/pubs/pubfiles/33.pdf) that is online at Stanley's website has some printing defects that make some of the pages illegible.


