In his book *Young Tableaux*, Fulton asserts, in Exercise 9.4.18 on p. 152, that the Schubert variety $\Omega\_{\lambda}$ is defined by the conditions $\text{dim}(V \cap F\_{n+i- \lambda\_{i}}) \geq i$ for those $i$ such that the coordinate $(i,\lambda\_{i})$ is an outside corner of the Young diagram $\lambda$. I take it that $F\_{\cdot}$ is the standard flag variety, and so the first initial part of this exercise makes sense in terms of the complex Grassmannian $Gr^{n}(E)=Gr\_{r}(E)$ with $E$ an $m$-dimensional complex vector space such that $m=n+r$, i.e. $$\Omega\_{\lambda}= \{V \in Gr^{n}(E): \text{dim}(V \cap F\_{n+i- \lambda\_{i}}) \geq i,1 \leq i \leq r\}.$$ However, how does one show that each $i$ is such that $(i,\lambda\_{i})$ is an outside corner of the Young diagram $\lambda$? It's difficult for me to visualize it. What are some good sources that might help to explain this better?



Schubert varieties and Young diagrams
All values of $(i,\lambda\_i)$ appear. The ones that aren't outside corners are redundant.


