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

I am interested in a description of orbits of the natural $GL(V)$ action on $V^{\otimes d}$. I know this is a classical problem but I tried to find some "good" reference and I couldn't. I'm also interested in orbits of the natural $S_d\times GL(V)$ action on $V^{\otimes d}$. I'm assuming characteristic $0$ but references in finite characteristic are also welcomed.

share|cite|improve this question
Can you say more precisely what motivates your third sentence: "I'm also interested ..."? This seems to get outside the usual literature on Schur-Weyl duality. Are there examples? – Jim Humphreys Feb 4 '13 at 23:51
up vote 9 down vote accepted

See, for instance, Chapter 5 of Goodman and Wallach's book "Symmetry, Representations and Invariants". Another good reference is Procesi's "Lie Groups: An approach through Invariants and Representations".

share|cite|improve this answer

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.