Spectrum of the $\bar{\mathrm{\partial }}$-Laplace operator on zero forms for the quantum quadric ${\mathcal{O}}_q({\mathbf{\text{Q}}}_N)$

We study the Laplacian operator ${\mathrm{\Delta }}_{\bar{\mathrm{\partial }}}$ associated to a Kähler structure $({\mathrm{\Omega }}^{(\bullet ,\bullet )},\kappa )$ for the Heckenberger–Kolb differential calculus of the quantum quadrics ${\mathcal{O}}_q({\mathbf{\text{Q}}}_N)$, which is to say, the irreducible quantum flag manifolds of types $B_n$ and $D_n$. We show that the eigenvalues of ${\mathrm{\Delta }}_{\bar{\mathrm{\partial }}}$ on zero forms tend to infinity and have finite multiplicity.