Conjecture 1 for the character of free Jordan algebras

Let $K$ be a field of characteristic zero and let $J(D)$ be the free Jordan algebra on $D\geq 1$ generators. Let $\operatorname{Inner}J(D)$ be its Lie algebra of inner derivations, and let $A(D)$ and $B(D)$ be the elements of ${\cal M}_{an}(GL(D))$ defined by the two character equations in Lemma.

Conjecture 1. In ${\cal R}_{an}(GL(D))$,

$$[J(D)]=A(D),\qquad [\operatorname{Inner}J(D)]=B(D).$$

This conjecture determines the $GL(D)$-characters of the homogeneous components of the free Jordan algebra and its inner derivation algebra; its dimension-only weak form is stated separately. The paper presents numerical evidence but does not establish the full character formula.