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- W3099879706 abstract "For a Kähler manifold $$M$$ , the “symplectic Dolbeault operators” are defined using the symplectic spinors and associated Dirac operators, in complete analogy to how the usual Dolbeault operators, $$bar{partial }$$ and $$bar{partial }^*$$ , arise from Dirac operators on the canonical complex spinors on $$M$$ . We give special attention to two special classes of Kähler manifolds: Riemann surfaces and flag manifolds ( $$G/T$$ for $$G$$ a simply-connected compact semisimple Lie group and $$T$$ a maximal torus). For Riemann surfaces, the symplectic Dolbeault operators are elliptic and we compute their indices. In the case of flag manifolds, we will see that the representation theory of $$G$$ plays a role and that these operators can be used to distinguish (as Kähler manifolds) between the flag manifolds corresponding to the Lie algebras $$B_n$$ and $$C_n$$ . We give a thorough analysis of these operators on $$mathbb{C } P^1$$ (the intersection of these classes of spaces), where the symplectic Dolbeault operators have an especially interesting structure." @default.
- W3099879706 created "2020-11-23" @default.
- W3099879706 creator A5051261443 @default.
- W3099879706 date "2013-03-09" @default.
- W3099879706 modified "2023-09-23" @default.
- W3099879706 title "Symplectic Dolbeault operators on Kähler manifolds" @default.
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- W3099879706 doi "https://doi.org/10.1007/s10455-013-9369-x" @default.
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