%0 Generic %1 chi1995incompleteness %A Chi, Quo-Shin %A Merkulov, Sergey A. %A Schwachhöfer, Lorenz J. %D 1995 %K bergers holonomy incompleteness representations %T On the Incompleteness of Berger's List of Holonomy Representations %U http://arxiv.org/abs/dg-ga/9508014 %X In 1955, Berger Ber gave a list of irreducible reductive representations which can occur as the holonomy of a torsion-free affine connection. This list was stated to be complete up to possibly a finite number of missing entries. In this paper, we show that there is, in fact, an infinite family of representations which are missing from this list, thereby showing the incompleteness of Berger's classification. Moreover, we develop a method to construct torsion-free connections with prescribed holonomy, and use it to give a complete description of the torsion-free affine connections with these new holonomies. We also deduce some striking facts about their global behaviour.

@misc{chi1995incompleteness, abstract = {In 1955, Berger \cite{Ber} gave a list of irreducible reductive representations which can occur as the holonomy of a torsion-free affine connection. This list was stated to be complete up to possibly a finite number of missing entries. In this paper, we show that there is, in fact, an infinite family of representations which are missing from this list, thereby showing the incompleteness of Berger's classification. Moreover, we develop a method to construct torsion-free connections with prescribed holonomy, and use it to give a complete description of the torsion-free affine connections with these new holonomies. We also deduce some striking facts about their global behaviour.}, added-at = {2013-12-23T06:28:58.000+0100}, author = {Chi, Quo-Shin and Merkulov, Sergey A. and Schwachhöfer, Lorenz J.}, biburl = {https://www.bibsonomy.org/bibtex/23dcaa6b8debad1d105611bc4c56c0e71/aeu_research}, description = {On the Incompleteness of Berger's List of Holonomy Representations}, interhash = {da0f2dd9afea597106e6dac135970ee2}, intrahash = {3dcaa6b8debad1d105611bc4c56c0e71}, keywords = {bergers holonomy incompleteness representations}, note = {cite arxiv:dg-ga/9508014Comment: 20 pages, AMS-LaTeX, no figures}, timestamp = {2013-12-23T06:28:58.000+0100}, title = {On the Incompleteness of Berger's List of Holonomy Representations}, url = {http://arxiv.org/abs/dg-ga/9508014}, year = 1995 }