Abstract
This paper studies the geometry of one-parameter specializations of subvarieties of Grassmannians and two-step flag varieties. As a consequence, we obtain a positive, geometric rule for expressing the structure constants of the cohomology of two-step flag varieties in terms of their Schubert basis. A corollary is a positive, geometric rule for computing the structure constants of the small quantum cohomology of Grassmannians. We also obtain a positive, geometric rule for computing the classes of subvarieties of Grassmannians that arise as the projection of the intersection of two Schubert varieties in a partial flag variety. These rules have numerous applications to geometry, representation theory and the theory of symmetric functions.
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Mathematics Subject Classification (2000)
Primary 14M15, 14N35, 32M10
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Coskun, I. A Littlewood–Richardson rule for two-step flag varieties. Invent. math. 176, 325–395 (2009). https://doi.org/10.1007/s00222-008-0165-3
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DOI: https://doi.org/10.1007/s00222-008-0165-3