Equivariant asymptotics of Szegö kernels under Hamiltonian $${{\varvec{U}}}(\mathbf{2})$$ U ( 2 ) -actions
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ID: 117256
2018
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Abstract
Let M be complex projective manifold and A a positive line bundle on it. Assume that a compact and connected Lie group G acts on M in a Hamiltonian manner and that this action linearizes to A. Then, there is an associated unitary representation of G on the associated algebro-geometric Hardy space. If the moment map is nowhere vanishing, the isotypical components are all finite dimensional; they are generally not spaces of sections of some power of A. One is then led to study the local and global asymptotic properties the isotypical component associated with a weight $$k \, \varvec{ \nu }$$ k ν , when $$k\rightarrow +\infty $$ k → + ∞ . In this paper, part of a series dedicated to this general theme, we consider the case $$G=U(2)$$ G = U ( 2 ) .
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galasso2018annaliequivariant
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| Authors | Andrea Galasso;Roberto Paoletti;Andrea Galasso;Roberto Paoletti; |
| Journal | annali di matematica pura ed applicata (1923 -) |
| Year | 2018 |
| DOI |
doi:10.1007/s10231-018-0791-3
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