Quantum gl(1/1) and tangle Floer homology

摘要

We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain U-q(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 U-q(gl(1/1)). (C) 2019 Elsevier Inc. All rights reserved.