The Last Possible Place of Unitarity for Certain Highest Weight Modules.
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
We introduce an explicit procedure to generate natural operators on manifolds with almost Hermitian symmetric structures and work out several examples of this procedure in the case of almost Grassmannian structures.