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Representations of a reductive algebraic group whose algebras of invariants are complete intersections. (English) Zbl 0575.20036
A linear representation $$\rho$$ of a complex reductive algebraic group G over $${\mathbb{C}}$$ is said to be COCI, if the algebra of invariant polynomial functions on the space of $$\rho$$ under the action of G is a complete intersection. We give a necessary condition for $$\rho$$ to be COCI, and using this, show that, if G is simple and simply connected and $$\rho$$ is COCI, then $$\rho$$ is coregular or one of $$(Sym^ 5\Phi,SL_ 2)$$, $$(Sym^ 6\Phi,SL_ 2)$$, $$(Sym^ 3\Phi,SL_ 4)$$ and $$(\Phi \cdot \Lambda^ 2\Phi,SL_ 4)$$.

##### MSC:
 20G05 Representation theory for linear algebraic groups 20G20 Linear algebraic groups over the reals, the complexes, the quaternions 15A72 Vector and tensor algebra, theory of invariants
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