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Irreducible holonomy representations. (English) Zbl 1037.53034
Slovák, Jan (ed.) et al., The proceedings of the 20th winter school “Geometry and physics”, Srní, Czech Republic, January 15–22, 2000. Palermo: Circolo Matematico di Palermo. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 66, 59-81 (2001).
This is a nice survey of the problem of classification of the irreducible holonomy groups of torsion free affine connections. This classification was finally obtained by S. Merkulov and the author [Ann. Math. (2) 150, 77–149 (1999; Zbl 0992.53038); Oxford University Press. 395–402 (1998; Zbl 0907.53018)]. In this paper the author in particular stresses his attention on the Merkulov twistor space associated to each holomorphic torsion free connection on a complex manifold and construction of special symplectic holonomies introduced by Chi, Merkulov, and the author.
For the entire collection see [Zbl 0961.00020].

MSC:
53C29 Issues of holonomy in differential geometry
53C05 Connections, general theory
53C28 Twistor methods in differential geometry
53C17 Sub-Riemannian geometry
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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