Arithmetic Constraints on Charges of Symmetric Monopoles
For Euclidean BPS monopoles with gauge group $SU(N)$, maximal symmetry breaking, and sufficiently generic spectral data, we produce necessary congruence relations that their magnetic charges must satisfy when $N \geq 3$. As such, a monopole as above with given charges can have certain subgroups of $SO(3)$ ruled out as possible groups of symmetries. In particular, the axially symmetric case may only admit non-trivial magnetic charges in the non-generic setting.
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