Geometry of Peterson Schubert calculus in type a and left-right diagrams. (English) Zbl 07841438
Summary: We introduce an additive basis of the integral cohomology ring of the Peterson variety which reflects the geometry of certain subvarieties of the Peterson variety. We explain the positivity of the structure constants from a geometric viewpoint, and provide a manifestly positive combinatorial formula for them. We also prove that our basis coincides with the additive basis introduced by Harada-Tymoczko.
MSC:
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
| 05E40 | Combinatorial aspects of commutative algebra |
References:
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