Geodesic
A Borel–Weil theorem for the quantum Grassmannians
Documenta mathematica, Tome 28 (2023) no. 2, pp. 261-314

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We establish a noncommutative generalisation of the Borel–Weil theorem for the celebrated 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 Kähler geometry of the quantum Grassmannians are also given.
DOI : 10.4171/dm/913
Classification : 46L87, 81R60, 81R50, 17B37, 16T05
Mots-clés : Quantum groups, noncommutative geometry, quantum flag manifolds, complex geometry 
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Alessandro Carotenuto; Colin Mrozinski; Réamonn Ó Buachalla. A Borel–Weil theorem for the quantum Grassmannians. Documenta mathematica, Tome 28 (2023) no. 2, pp. 261-314. doi: 10.4171/dm/913

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