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

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?

share|improve this question
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.