Quantum gl(1|1) and tangle Floer homology
Abstract
We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain Uq(gl(1|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 Uq(gl(1|1)).
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