Probing Lepton-Number Violating Couplings of Doubly Charged Higgs Bosons at an $e^-e^-$ Collider

The doubly charged Higgs bosons $\Delta^{--}$ that are present in exotic Higgs representations can have lepton-number-violating couplings to $e^-e^-$. We discuss general constraints and phenomenology for the $\Delta^{--}$ and demonstrate that extremely small values for the $e^-e^-\rightarrow\Delta^{--}$ coupling (some 8 orders of magnitude smaller than the current limit) would produce observable signals for $\Delta^{--}$ production in direct $s$-channel production at an $e^-e^-$ collider.