Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
For the action of $GL(n) × GL(m)$ on $C[Mat(n × m)]$, the polynomial functions on $n × m$ matrices, what are the functions which are the highest weight vectors with respect to both $GL(n)$ and $GL(m)$?