On birational automorphisms of double EPW‐cubes

Abstract We give a classification of finite groups of symplectic birational automorphisms on manifolds of ‐type with stable cohomological action. We describe the group of polarized automorphisms of a smooth double EPW‐cube. Using this description, we exhibit examples of projective hyperkähler manifolds of –type of maximal Picard rank with a symplectic action of a large group.