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The Combinatorics of Steenrod Operations on the Cohomology of Grassmannians

✍ Scribed by Cristian Lenart

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
643 KB
Volume
136
Category
Article
ISSN
0001-8708

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✦ Synopsis

The study of the action of the Steenrod algebra on the mod p cohomology of spaces has many applications to the topological structure of those spaces. In this paper we present combinatorial formulas for the action of Steenrod operations on the cohomology of Grassmannians, both in the Borel and the Schubert picture. We consider integral lifts of Steenrod operations, which lie in a certain Hopf algebra of differential operators. The latter has been considered recently as a realization of the Landweber Novikov algebra in complex cobordism theory; it also has connections with the action of the Virasoro algebra on the boson Fock space. Our formulas for Steenrod operations are based on methods which have not been used before in this area, namely Hammond operators and the combinatorics of Schur functions. We also discuss applications of our formulas to the geometry of Grassmannians.

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