Dixmier Trace for Toeplitz Operators on Symmetric Domains

For Toeplitz operators on bounded symmetric domains of arbitrary rank, we define a Hilbert quotient module corresponding to partitions of length $1$ and prove that it belongs to the Macaev class ${\mathcal{L}}^{n,\mathrm{\infty }}$. We next obtain an explicit formula for the Dixmier trace of Toeplitz commutators in terms of the underlying boundary geometry.