Spectrum of the [formula omitted]-Laplace operator on zero forms for the quantum quadric [formula omitted]

Abstract

We study the Laplacian operator Δ∂‾ associated to a Kähler structure (Ω(•,•),κ) for the Heckenberger–Kolb differential calculus of the quantum quadrics Oq(QN), which is to say, the irreducible quantum flag manifolds of types Bn and Dn. We show that the eigenvalues of Δ∂‾ on zero forms tend to infinity and have finite multiplicity.