K-polystable smooth Fano threefolds with ample Q-divisor polarization have reductive automorphism groups.
Malbon,Automorphisms of Fano threefolds of rank 2 and degree 28, Annali dell’Universita di Ferrara70 (2024), 1083–1092
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A Matsushima theorem for K-polystable polarised smooth Fano threefolds
K-polystable smooth Fano threefolds with ample Q-divisor polarization have reductive automorphism groups.