The Horn problem for Symmetric Real and Quaternionic Self-Dual Matrices

The notations are those of [Coquereaux-Zuber arXiv:1809.xxxx]:

The four polynomials giving the piece-wise expression of J₃

In the generic case, the resultant R of the two polynomials P_p(c) and Q_q(c) is given here in pdf and in Mathematica notebook form.

In the particular case, α= β=(1,0,-1),
the discriminant Δ_R of R takes the following pdf or notebook form,
and the discriminant Δ⁽²⁾_R of Δ⁽¹⁾_R with respect to z is given here in pdf or notebook form.