Geodesic
The Universal Connection for Principal Bundles over Homogeneous Spaces and Twistor Space of Coadjoint Orbits
Documenta mathematica, Tome 23 (2018), pp. 77-115
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Given a holomorphic principal bundle Q⟶X, the universal space of holomorphic connections is a torsor C1​(Q) for adQ⊗T∗X such that the pullback of Q to C1​(Q) has a tautological holomorphic connection. When X=G/P, where P is a parabolic subgroup of a complex simple group G, and Q is the frame bundle of an ample line bundle, we show that C1​(Q) may be identified with G/L, where L⊂P is a Levi factor. We use this identification to construct the twistor space associated to a natural hyper-Kähler metric on T∗(G/P), recovering Biquard's description of this twistor space, but employing only finite-dimensional, Lie-theoretic means.
DOI : 10.4171/dm/614
Classification : 14M17, 32L10, 32L25
Mots-clés : rational homogeneous space, twistor space, λ-connection, complexification, Levi subgroup 
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     author = {Indranil Biswas and Michael Lennox Wong},
     title = {The {Universal} {Connection} for {Principal} {Bundles} over {Homogeneous} {Spaces} and {Twistor} {Space} of {Coadjoint} {Orbits}},
     journal = {Documenta mathematica},
     pages = {77--115},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/614},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/614/}
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Indranil Biswas; Michael Lennox Wong. The Universal Connection for Principal Bundles over Homogeneous Spaces and Twistor Space of Coadjoint Orbits. Documenta mathematica, Tome 23 (2018), pp. 77-115. doi: 10.4171/dm/614

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