Scaling asymptotics of Szegö kernels under commuting Hamiltonian actions (Q343503)

Let \(M\) be a complex projective manifold, with commuting holomorphic Hamiltonian actions of a compact Lie group \(G\) and a compact torus \(T\), which both linearize to a holomorphic positive Hermitian line bundle. The author studies the local scaling asymptotics of the equivariant Szegö kernels when the irreducible representation of \(T\) tends to infinity along a ray and the irreducible representation of \(G\) is held fixed, investigating their asymptotic concentration along certain loci defined by the moment maps.