Tensor Representations of ${\mathfrak {q}} (\infty )$

Abstract

We introduce a symmetric monoidal category of modules over the direct limit queer superalgebra ${\mathfrak{q}}(\infty )$. This category can be defined in two equivalent ways with the aid of the large annihilator condition. Tensor products of copies of the natural and the conatural representations are injective objects in this category. We obtain the socle filtrations and formulas for the tensor products of the indecomposable injectives. In addition, it is proven that the category is Koszul self-dual.