Advances in Theoretical and Mathematical Physics

Quantization of flag manifolds and their supersymmetric extensions

Séan Murray and Christian Sämann

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Abstract

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

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

Dates
First available in Project Euclid: 7 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1210167655

Mathematical Reviews number (MathSciNet)
MR2399321

Zentralblatt MATH identifier
1149.81020

Citation

Murray, Séan; Sämann, Christian. Quantization of flag manifolds and their supersymmetric extensions. Adv. Theor. Math. Phys. 12 (2008), no. 3, 641--710. https://projecteuclid.org/euclid.atmp/1210167655


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