Hamiltonian spectral invariants, symplectic spinors and Frobenius structures I
This is the first of two articles aiming to introduce symplectic spinors into the field of symplectic topology and the subject of Frobenius structures. After exhibiting a (tentative) axiomating setting for Frobenius structures resp. ’Higgs pairs’ in the context of symplectic spinors, we present immediate observations concerning a local Schroedinger equation, the first structure connection and the existence of ’spectrum’, its topological interpretation and its connection to ’formality’ which are valid for the case of standard Frobenius structures. We give a classification of the irreducibles and the indecomposables of the latter in terms of certain U(n)-reductions of the G-extension of the metaplectic frame bundle and a certain connection on it, where G is the semi-direct product of the metaplectic group and the Heisenberg group, while the indecomposable case involves in addition the combinatorial structure of the eigenstates of the n-dimensional harmonic oscillator. In the second ∗