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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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