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We describe the structure of the tensor product of the basic Fockrepresentation of sl(\infty) with its shifted dual. More precisely we provethat this tensor product has a unique decreasing filtration with simplequotients. We use the categorification of this representation via translationfunctors in the abelain envelope of the Deligne category GL(t) for integral t.We also compute dimensions of standard and tilting objects in this abelianenvelope.

Tensor product of the Fock representation with its dual and the Deligne category