1997/07/11 by Cristian Lenart, Lenart, Cristian
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT
paper · pdf · doi:10.48550/arxiv.math/9707219
openalex publication_date 1997/07/11 · arxiv created 1997/07/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The study of the action of the Steenrod algebra on the mod p cohomology of\nspaces has many applications to the topological structure of those spaces. In\nthis paper we present combinatorial formulas for the action of Steenrod\noperations on the cohomology of Grassmannians, both in the Borel and the\nSchubert picture. We consider integral lifts of Steenrod operations, which lie\nin a certain Hopf algebra of differential operators. The latter has been\nconsidered recently as a realization of the Landweber-Novikov algebra in\ncomplex cobordism theory; it also has connections with the action of the\nVirasoro algebra on the boson Fock space. Our formulas for Steenrod operations\nare based on combinatorial methods which have not been used before in this\narea, namely Hammond operators and the combinatorics of Schur functions. We\nalso discuss several applications of our formulas to the geometry of\nGrassmannians.\n