is not a base form
Notice that symmetries form a Lie superalgebra:
This superalgebra acts on .
However, it turns out that is not a base form with respect to symmetries. More precisely:
is invariant but not horizontal
Therefore we cannot integrate over cycles in the base:
does not descend to a PDF on the coset
We factorize over symmetries, but not over all symmetries. We will identify a subgroup in the group of symmeties, which has the properties:
It is large enough for the factorspace to have interesting integration cycles.
It is small enough to allow us to define a closed base PDF which we will call .