On a Koszul complex related to the principal subspace of the basic vacuum module for A1(1)

We analyze a certain Koszul complex related to the principal subspace of the level 1 vacuum standard module for the affine Lie algebra A1(1). We determine the second homology of this Koszul complex. A complete description of the Koszul homology is expected to yield a certain new character formula for the principal subspace. We relate our results to the Garland-Lepowsky resolution of the ambient standard module and to Gorsky, Oblomkov and Rasmussen's recent conjectures on the stable Khovanov homology of the torus knots.