Subgroups Generated by a Pair of 2-Tori in GL(4,K), II

The present paper is another work of major cycle of works devoted to the geometry of microweight tori in the Chevalley groups. Namely, we describe the subgroups generated by a pair of 2-tori in GL(4,K). Recall that 2-tori in GL(n,K) are the subgroups conjugate to the diagonal subgroup of the following form diag(ε, ε, 1,, 1). In one of the previous work we proved the reduction theorem for the pairs of m-tori. It follows from it that any pair of 2-tori can be embedded in GL(6,K) by simultaneous conjugation. The orbit of a pair of 2-tori $(X,Y)$ is called the orbit in GL(n,K), if the pair $(X,Y)$ is embedded in GL(n,K) by simultaneous conjugation and it can not be embedded in GL(n-1,K). Here n can take values 3, 4, 5 and 6. The most difficult and general case is the case of GL(4,K). In the present manuscript we describe spans in GL(4,K), corresponding to degenerate orbits.