A sufficient condition for a Hibi ring to be level and levelness of Schubert cycles
نویسنده
چکیده
Let K be a field, D a finite distributive lattice and P the set of all join-irreducible elements of D. We show that if {y ∈ P | y ≥ x} is pure for any x ∈ P , then the Hibi ring RK(D) is level. Using this result and the argument of sagbi basis theory, we show that the homogeneous coordinate rings of Schubert subvarieties of Grassmannians are level. MSC:13F50, 13H10, 13A02, 14M15, 13P10
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