Quantum supergroups. IV: The modified form (Q463988)

The paper under review constructs a canonical basis for a class of tensor product modules for a quantum covering group associated to a Kac-Moody Lie superalgebra of anisotropic type. These bases are then used to construct a canonical basis for the modified form (a.k.a. the idempotented version) of a quantum covering group. The paper also defines a bilinear form on the modified quantum covering group which generalizes the bilinear form on the half-quantum covering group. This bilinear form is shown to be invariant under some automorphisms of the quantum covering group, and it can be viewed as a limit of bilinear forms on the tensor product modules. For Parts I--III and V, see Zbl 1359.17023, Zbl 1359.17024, Zbl 1359.17022, Zbl 1364.17016.