Diagrams for geometries and groups

Geometries from Young Diagrams

Type IIB string theory on spacetimes that are asymptotically AdS5×S can be defined using four dimensional N = 4 super Yang-Mills theory. Six of the dimensions of the string theory are holographically reconstructed in the Yang-Mills theory. In this article we study how these dimensions and local physics in these dimensions emerge. We reorganize the dynamics of the 1 2 BPS sector of the field the...

Groups for Geometries in Given Diagrams, II: on a Characterization of the Group Aut(HS)

This paper is a continuation of [12): we begin to carry out the programme outlined in [12), adapting a more detailed approach. In this paper a geometry discovered by S. Yoshiara [19) and admitting Aut(HS) as automorphism group is considered. The interest of this geometry also lies in certain 'irregular' features, which give it an exceptional position among other c. C2 geometries. The uniqueness...

Diagrams and groups

Zariski Theorems and Diagrams for Braid Groups

Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Broué-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is invariant-theoretic and does not use the cla...

Automorphism Groups of Parabolic Geometries

We show that elementary algebraic techniques lead to surprising results on automorphism groups of Cartan geometries and especially parabolic geometries. The example of three–dimensional CR structures is discussed in detail.