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A eutactic star on an integral lattice is called extremal if it induces aholomorphic Jacobi form of lattice index and singular weight via the thetablock. The famous Macdonald identities imply that root systems are extremal aseutactic stars. In this paper we prove that every extremal eutactic star arisesas a root system. This answers a question posed by Skoruppa.

There are no extremal eutactic stars other than root systems