Advances in Theoretical and Mathematical Physics

Quantization of flag manifolds and their supersymmetric extensions

Séan Murray and Christian Sämann

Full-text: Open access


We first review the description of flag manifolds in terms of Plücker 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 Plücker 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.

Article information

Adv. Theor. Math. Phys., Volume 12, Number 3 (2008), 641-710.

First available in Project Euclid: 7 May 2008

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Murray, Séan; Sämann, Christian. Quantization of flag manifolds and their supersymmetric extensions. Adv. Theor. Math. Phys. 12 (2008), no. 3, 641--710.

Export citation