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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 invari …

Let $T=(\mathbb{C}^{\times})^n$ be the $n$-dimensional torus acting on the polynomial algebra $\mathbb{C}[x_1,x_2, \ldots,x_n]$ diagonally, i.e. $$ diag(t^{a_1},t^{a_2},\ldots,t^{a_n})x_i=t^{a_i}x_i, …

See the preprint The MAPLE package for SL2-invariants and kernel of Weitzenböck derivations

The separating set coincides with the field of semi-invariants and the last can be easy computed in an explicit way for any degree $d.$ Precisely, it generated by elements $$ a_0,z_2,z_3,\ldots,z_d, …

Let $V_d$ be the complex vector space of binary forms of degree $d$ endowed with the natural action of the special orthogonal group $SO(2).$ Consider the corresponding action of the group $SO(2)$ on …