A Borel–Weil theorem for the quantum Grassmannians

  • Alessandro Carotenuto

    Masaryk University, Brno, Czech Republic
  • Colin Mrozinski

    Polskiej Akademii Nauk, Warsaw, Poland
  • Réamonn Ó Buachalla

    Mathematical Institute of Charles University, Prague, Czech Republic
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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.

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Alessandro Carotenuto, Colin Mrozinski, Réamonn Ó Buachalla, A Borel–Weil theorem for the quantum Grassmannians. Doc. Math. 28 (2023), no. 2, pp. 261–314

DOI 10.4171/DM/913