Pair-zero and degree conditions admit extra six-dimensional hook solutions at seven points and a two-dimensional plane at eight; Bose symmetry and one normalized physical boundary condition single out the Hodges numerator.
A geometric approach to Standard Monomial Theory
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abstract
We obtain a geometric construction of a ``standard monomial basis'' for the homogeneous coordinate ring associated with any ample line bundle on any flag variety. This basis is compatible with Schubert varieties, opposite Schubert varieties, and unions of intersections of these varieties. Our approach relies on vanishing theorems and a degeneration of the diagonal ; it also yields a standard monomial basis for the multi-homogeneous coordinate rings of flag varieties of classical type.
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Algebraic versus physical uniqueness of MHV gravity numerators
Pair-zero and degree conditions admit extra six-dimensional hook solutions at seven points and a two-dimensional plane at eight; Bose symmetry and one normalized physical boundary condition single out the Hodges numerator.