In the paper under review, the author presents some results on the basis of the Nash-Gromov theory of isometric immersions and illustrates how the same results and ideas can be extended to other structures.

We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...

A flag manifold of a compact semisimple Lie group $G$ is defined as a quotient $M=G/K$ where $K$ is the centralizer of a one-parameter subgroup $exp\left(tx\right)$ of $G$. Then $M$ can be identified with the adjoint orbit of $x$ in the Lie algebra $𝒢$ of $G$. Two flag manifolds $M=G/K$ and $M^{\text{'}}=G/K^{\text{'}}$ are equivalent if there exists an automorphism $\phi :G\to G$ such that $\phi \left(K\right)=K^{\text{'}}$ (equivalent manifolds need not be $G$-diffeomorphic since $\phi$ is not assumed to be inner). In this article, explicit formulas for decompositions of the isotropy representation for all flag manifolds...