A Borel-Weil theorem for the quantum Grassmannians

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Authors

CAROTENUTO Alessandro MROZINSKI Colin BUACHALLA Réamonn Ó.

Year of publication 2023
Type Article in Periodical
Magazine / Source Documenta Mathematica
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.4171/dm/913
Doi http://dx.doi.org/10.4171/DM/913
Keywords Quantum groups; noncommutative geometry; quantum flag manifolds; complex geometry
Description 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.
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