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In this paper, we relate umbral moonshine to the Niemeier lattices - the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice, we attach a finite group by considering a naturally defined quotient of the lattice automorphism group, and for each conjugacy class of each of these groups, we identify a vector-valued mock modular form whose components...
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