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Let $V_\lambda$ be an irreducible representation of the symmetric group $S_n$ as usual labeled by parition $\lambda$ of $n.$

Question. Is there any general information about the algebra of invariants $\mathbb{C}[V_\lambda]^{S_n}$: minimal generating set, number of generators, constructive algorithms, usefull isomorphisms, Hilbert series?

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  • $\begingroup$ The Hilbert series of $\mathbb{C}[V]^G$ for any finite-dimensional representation of any finite (or even compact) group $G$ can be computed using Molien's theorem: en.wikipedia.org/wiki/Molien_series $\endgroup$
    – Qiaochu Yuan
    Commented Jul 5, 2014 at 21:16
  • $\begingroup$ Of cource, but did you see such calculations for $\mathbb{C}[V_\lambda]^{S_n}$ ? any reference, please $\endgroup$
    – Leox
    Commented Jul 5, 2014 at 22:16

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