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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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votes
Is $Sym^n (V^*) \cong Sym^n (V)^\ast$ naturally in positive characteristic?
The dual to symmetric powers of a projective module of finite rank over any commutative ring is most elegantly expressed in terms of divided powers (thereby also "explaining" why over a field of nonze …