The second Seeley–DeWitt coefficient of the scalar Laplacian on the E₈ Wolf space EIX

We compute the second Seeley–DeWitt heat-kernel coefficient a₂ of the scalar Laplacian on the 112-dimensional quaternion-Kähler Wolf space EIX = E₈/(E₇ × SU(2)), equipped with the canonical E₈-invariant metric. The key ingredient is the evaluation of |Riem|² via the Schur lemma applied to the isotropy module m ≅ (56, 2): the Schur eigenvalues on the two simple ideals of the isotropy algebra equal the differences of dual Coxeter numbers, cE₇ = h∨{E₈} − h∨{E₇} = 12 and cSU(2) = h∨{E₈} − h∨{SU(2)} = 28. This gives |Riem|² = 21 504 and a₂(EIX) = 587 692 / 15 ≈ 39 179.47.