Schubert Calculus and the Homology of the Peterson Variety

Erik Insko

Abstract


We use the tight correlation between the geometry of the Peterson variety and the combinatorics the symmetric group to prove that homology of the Peterson variety injects into the homology of the flag variety. Our proof counts the points of intersection between certain Schubert varieties in the full flag variety and the Peterson variety, and shows that these intersections are proper and transverse.


Keywords


Schubert calculus; Intersection theory; Peterson variety; Schubert varieties

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