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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:mathematical_concept
gptkb:homogeneous_space
gptkb:Kähler_manifold
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gptkbp:appearsIn
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gptkb:moduli_problems
gptkb:quantum_cohomology
enumerative geometry
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gptkbp:can_be_realized_as
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quotient space U(n)/(U(k) × U(n-k))
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gptkbp:compact
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true
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gptkbp:connectedTo
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true
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gptkbp:definedIn
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space of all k-dimensional linear subspaces of complex n-dimensional space
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gptkbp:dimensions
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k(n-k)
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gptkbp:generalizes
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complex projective space
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gptkbp:has_cell_decomposition
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gptkb:Schubert_cells
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gptkbp:has_cohomology_ring
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generated by Schubert classes
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gptkbp:has_Plücker_embedding
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into projective space
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gptkbp:hasSpecialCase
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Gr(1, n; C) is complex projective space CP^{n-1}
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gptkbp:is_homogeneous_space_for
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gptkb:unitary_group_U(n)
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gptkbp:notation
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Gr(k, n; C)
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gptkbp:relatedTo
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flag variety
real Grassmannian
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gptkbp:structure
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gptkb:projective_variety
gptkb:Kähler_manifold
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gptkbp:used_in
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gptkb:algebraic_geometry
differential geometry
representation theory
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gptkbp:bfsParent
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gptkb:compact_Hermitian_symmetric_space
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gptkbp:bfsLayer
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9
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https://www.w3.org/2000/01/rdf-schema#label
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complex Grassmannian
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