Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

The ordinary Grassmannian of k-planes in n-space is a coset space for $GL_n$. It is $GL_n$ mod a maximal parabolic. Here there is a nice basis given by Schubert varieties, which can be indexed by Young diagrams that fit in an (k)x(n-k) box. The structure constants for the cup product are then given by Littlewood-Richardson numbers.

My question: is there a similarly nice picture for Grassmannians of arbitrary simple groups. Here the ordinary Grassmannian is replaced by $G/P$ where $G$ is a simple group and $P$ is a maximal parabolic. There are still Schubert varieties in this case, but I don't know how to say anything about the cup product.

share|improve this question

1 Answer 1

up vote 14 down vote accepted

As yet, such a nice rule has only been formulated in the case that $G/P$ is minuscule or co-minuscule. See Thomas and Yong for details.

share|improve this answer
1  
...and I was just trying to work exactly this out. Good reference, David. –  Charles Siegel Nov 9 '09 at 18:25

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.