atlas · hodge_branch_std
One column per level of the filtration. Change ν and the K-types move: past each reducibility point every level drops, and the mass migrates to the left.
The top line is the highest weight for K0, coloured by its level; below it the atlas KGB element x, the parameter λ, the height and the dimension. A ×2 badge is multiplicity at that level.
Its Hodge polynomial has several terms. At ν = 0 the K-type x=4, λ=[3,2] is +v^4+2v^6: once in column 4, twice in column 6.
These are the 16 K-types of height at most 10, from hodge_branch_std(p,10). The representation is infinite dimensional; the counts below only cover what is shown.