Suppose we have a Lie group, \(G\), and most importantly, there does *not* exist any continuous, injective homomorphism of $G$ into any $GL(n; \mathbb C)$. Are there any physical theories for which there is such a Lie group $G$ as a symmetry? Or does any such type of group appear in physics more generally?

One example I have been able to find is that the metaplectic group, that is, the double cover of $Sp_{2n}$, arises in the context of duality groups, and indeed it is not isomorphic to any matrix Lie group.