MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
I've merged your accounts. If you register, you won't need to worry about making new user ids. – S. Carnahan Apr 25 '12 at 6:08

For a related question, invariants of the action of $G$ on the space of pairs of {1,...,n}, (this is a quotient ring of $C[V]^{G}$) see Sect. 2 of Algebraic invariants of graphs; a study based on computer exploration, by Nicolas M. Thiéry. However, the generating set given there is certainly very far from a minimal, and degrees are high. Sect. 10 of this paper also discusses the ring you are asking about.

share|cite|improve this answer
@Dima: excellent reference. It seems to me that the ring in Ketan's question is exactly the Grigoriev digraph invariant ring mentioned in Section 10 of Thiery's article. – Abdelmalek Abdesselam Apr 23 '12 at 16:19

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

share|cite|improve this answer
Are you your own evil twin? There seem to be two KMs with different reps... – Igor Rivin Apr 23 '12 at 13:28

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.