most recent 30 from http://mathoverflow.net 2013-05-21T18:49:54Z http://mathoverflow.net/feeds/question/4745 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/4745/littlewood-richardson-type-rule-for-cohomology-ring-of-grassmannians Dinakar Muthiah 2009-11-09T17:15:49Z 2009-11-09T17:19:04Z

<p>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.</p> <p>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.</p>

http://mathoverflow.net/questions/4745/littlewood-richardson-type-rule-for-cohomology-ring-of-grassmannians/4747#4747 David Speyer 2009-11-09T17:19:04Z 2009-11-09T17:19:04Z

<p>As yet, such a nice rule has only been formulated in the case that $G/P$ is minuscule or co-minuscule. See <a href="http://front.math.ucdavis.edu/0608.5276" rel="nofollow">Thomas and Yong</a> for details.</p>