zbMATH — the first resource for mathematics

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].

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)