A Borel–Weil theorem for the quantum Grassmannians Article Swipe

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Noncommutative geometry Mathematics Holomorphic function Pure mathematics Grassmannian Quantum differential calculus Noncommutative algebraic geometry Quantum Noncommutative quantum field theory Projective space Algebra over a field Cohomology ring Cohomology Projective test Equivariant cohomology Quantum mechanics Physics

Alessandro Carotenuto , Colin Mrozinski , Réamonn Ó Buachalla ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.4171/dm/913 · OA: W2552697260

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.