The quadratic type of the 2-principal indecomposable modules of the double covers of alternating groups

The principal indecomposable modules of the double cover 2.An of the alternating group over a field of characteristic 2 are enumerated using the partitions of n into distinct parts. We determine which of these modules afford a non-degenerate 2.An-invariant quadratic form. Our criterion depends on the alternating sum and the number of odd parts of the corresponding partition.