TITLE: Explicit generators for matrix invariants of the symmetric group
QUESTION [12 upvotes]: Let $V$ be the space of $n$ by $n$ complex matrices with the conjugate  action of the symmetric group $G=S_n$. Is any explicit set of generators for the invariant ring $C[V]^G$ known?

REPLY [3 votes]: thanks for all the answers. I found a paper by Garcia and Stanton, "Group actions on 
Stanley Reisner rings and .." (Advances in Maths, 1984), which provides a reasonable answer to this
question. 
Ketan Mulmuley