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arXiv · 1611.07969

A Borel-Weil Theorem for the Quantum Grassmannians

Alessandro Carotenuto·Colin Mrozinski·Réamonn Ó Buachalla
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Abstract

We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the quantum Grassmannians. The result is formulated in the framework of quantum principal bundles and noncommutative complex structures, and generalises previous work of a number of authors on quantum projective space. As a direct consequence we get a novel noncommutative differential geometric presentation of the twisted Grassmannian coordinate ring studied in noncommutative projective geometry. A number of applications to the noncommutative K\"ahler geometry of the quantum Grassmannians are also given.

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BibTeXRIS

Alessandro Carotenuto, Colin Mrozinski, Réamonn Ó Buachalla. 2016-11-23. A Borel-Weil Theorem for the Quantum Grassmannians. https://arxiv.org/abs/1611.07969

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