A Borel-Weil theorem for the quantum Grassmannians

0582933 - MÚ 2024 RIV DE eng J - Článek v odborném periodiku
Carotenuto, Alessandro - Mrozinski, C. - Buachalla, R. Ó.
A Borel-Weil theorem for the quantum Grassmannians.
Documenta Mathematica. Roč. 28, č. 2 (2023), s. 261-314. ISSN 1431-0643. E-ISSN 1431-0643
Grant CEP: GA ČR(CZ) GJ20-17488Y
Institucionální podpora: RVO:67985840
Klíčová slova: complex geometry * noncommutative geometry * quantum flag manifolds
Obor OECD: Pure mathematics
Impakt faktor: 0.9, rok: 2022
Způsob publikování: Open access
https://doi.org/10.4171/dm/913

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.
Trvalý link: https://hdl.handle.net/11104/0350976