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We study the emergence of odd-frequency superconducting pairing in UPt$_3$.Starting from a tight-binding model accounting for the nonsymmorphic crystalsymmetry of UPt$_3$ and assuming an order parameter in the $E_{2u}$representation, we demonstrate that odd-frequency pairing arises verygenerally, as soon as inter-sublattice hopping or spin-orbit coupling ispresent. We also show that in the low temperature superconducting $B$ phase,the presence of a chiral order parameter together with spin-orbit coupling,leads to additional odd-frequency pair amplitudes not present in the $A$ or $C$phases. Furthermore, we show that a finite Kerr rotation in the $B$ phase isonly present if odd-$\omega$ pairing also exists.

Odd-frequency pairing and Kerr effect in the heavy-fermion superconductor UPt$_3$