Quantization of Flag Manifolds and their Supersymmetric Extensions

Details Quantization of Flag Manifolds and their Supersymmetric Extensions Quantization of Flag Manifolds and their Supersymmetric Extensions

2006-11-29

arxiv.org/abs/hep-th/0611328v2

Adv.Theor.Math.Phys.12:641-710,2008

Physics

High Energy Physics

High Energy Physics - Theory

1+53 pages, 6 figures, version published in ATMP

Scientific paper

We first review the description of flag manifolds in terms of Pluecker coordinates and coherent states. Using this description, we construct fuzzy versions of the algebra of functions on these spaces in both operatorial and star product language. Our main focus is here on flag manifolds appearing in the double fibration underlying the most common twistor correspondences. After extending the Pluecker description to certain supersymmetric cases, we also obtain the appropriate deformed algebra of functions on a number of fuzzy flag supermanifolds. In particular, fuzzy versions of Calabi-Yau supermanifolds are found.

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