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Invariant theory deals with an algebraic, geometric or analytic structure $X$, submitted to the action of an (algebraic) group $G$. It studies $G$-invariant elements of $X$ as well as the set of $G$-orbits.
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0
answers
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Rational torus invariants
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.
$$
diag(t^{a_1},t^{a_2},\ldots,t^{a_n})x_i=t^{a_i}x_i, …
2
votes
0
answers
388
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Invariants of the group $SO(2)$
Let $V_d$ be the complex vector space of binary forms of degree $d$ endowed with the natural
action of the special orthogonal group $SO(2).$ Consider the corresponding action of the
group $SO(2)$ on …
0
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Explicit formulas for invariants of binary quintic forms
See the preprint The MAPLE package for SL2-invariants and kernel of Weitzenböck derivations
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Equivalent binary forms
The separating set coincides with the field of semi-invariants and the last can be easy computed in an explicit way for any degree $d.$
Precisely, it generated by elements
$$
a_0,z_2,z_3,\ldots,z_d, …
4
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0
answers
257
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Invariants of the symmetric group
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 …