| CAROTENUTO, Alessandro, Colin MROZINSKI and Réamonn Ó. BUACHALLA. A Borel-Weil theorem for the quantum Grassmannians. Documenta Mathematica. EMS Press, 2023, vol. 28, No 2, p. 261-314. ISSN 1431-0635. Available from: https://dx.doi.org/10.4171/DM/913. |
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@article{2317139,
author = {Carotenuto, Alessandro and Mrozinski, Colin and Buachalla, Réamonn Ó.},
article_number = {2},
doi = {http://dx.doi.org/10.4171/DM/913},
keywords = {Quantum groups; noncommutative geometry; quantum flag manifolds; complex geometry},
language = {eng},
issn = {1431-0635},
journal = {Documenta Mathematica},
title = {A Borel-Weil theorem for the quantum Grassmannians},
url = {https://doi.org/10.4171/dm/913},
volume = {28},
year = {2023}
}
TY - JOUR
ID - 2317139
AU - Carotenuto, Alessandro - Mrozinski, Colin - Buachalla, Réamonn Ó.
PY - 2023
TI - A Borel-Weil theorem for the quantum Grassmannians
JF - Documenta Mathematica
VL - 28
IS - 2
SP - 261-314
EP - 261-314
PB - EMS Press
SN - 14310635
KW - Quantum groups
KW - noncommutative geometry
KW - quantum flag manifolds
KW - complex geometry
UR - https://doi.org/10.4171/dm/913
N2 - 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.
ER -
CAROTENUTO, Alessandro, Colin MROZINSKI and Réamonn Ó. BUACHALLA. A Borel-Weil theorem for the quantum Grassmannians. \textit{Documenta Mathematica}. EMS Press, 2023, vol.~28, No~2, p.~261-314. ISSN~1431-0635. Available from: https://dx.doi.org/10.4171/DM/913.
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