On semi-invariants and index for biparabolic (seaweed) algebras, II

In a continuation of I, we study the semi-invariant subalgebra of for a biparabolic subalgebra of a semisimple or of an affine Lie algebra. In most cases this is shown to be polynomial and we compute the degrees and weights of the generators. We describe explicitly the canonical truncation of for which . Let denote the nilradical of and its derived algebra. We show that the subalgebra of is always polynomial and describe the degrees and weight of the generators. Finally a sum rule is given for the “false” degrees of . These are true degrees in most cases.