Szegö kernel equivariant asymptotics under Hamiltonian Lie group actions (Q2075357)

From the paper's abstract: ``Suppose that a compact and connected Lie group \(G\) acts on a complex Hodge manifold \(M\) in a holomorphic and Hamiltonian manner, and that the action linearizes to a positive holomorphic line bundle \(A\) on \(M\). Then there is an induced unitary representation on the associated Hardy space and, if the moment of the action is nowhere vanishing, the corresponding isotypical components are all finite dimensional. We study the asymptotic concentration behaviour of the corresponding equivariant Szegö kernels near certain loci defined by the moment map.'' The theorems obtained in this paper extend the asymptotic results obtained by the author previously in a series of papers (some jointly with Galasso), from the case when \(G\) is a torus or \(\mathrm{SU}(2)\) or \(\mathrm{U}(2)\) to the case when \(G\) is a compact connected Lie group which is ``acceptable'' (this condition is satisfied, in particular, when \(G\) is \(\mathrm{U}(n)\) for some \(n\ge 1\) or when \(G\) is a connected and simply connected compact semisimple Lie group).