most recent 30 from http://mathoverflow.net 2013-05-21T15:07:07Z http://mathoverflow.net/feeds/question/88435 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88435/distribution-of-young-diagrams JM Landsberg 2012-02-14T15:16:42Z 2012-02-14T15:16:42Z

<p>Consider $\Lambda^p(C^n\otimes C^n)=\oplus_{\pi}S_{\pi}C^n\otimes S_{\pi'}C^n$ as a $GL_n\times GL_n$-module. This space has dimension $\binom {n^2}p$. I would like any information on the shapes of pairs of diagrams $(\pi,\pi')$ that give the largest contribution to the dimension asymptotically. I am most interested in the case where $p$ is near $n^2/2$. Is there a slowly growing function $f(n)$ such that partitions with fewer than $f(n)$ steps contribute negligibly? If so, can the fastest growing such $f$ be determined?</p>