Quantum gl(1|1) and tangle Floer homology

We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain $U_q(gl(1\mathrm{\mid }1))$ representations. Under this identification, up to a scalar factor, the map on the Grothendieck group induced by the tangle Floer dg bimodule associated to a tangle agrees with the Reshetikhin-Turaev homomorphism for that tangle. We also introduce dg bimodules which act on the Grothendieck group as the generators $E$ and $F$ of $U_q(gl(1\mathrm{\mid }1))$.