The Schubert calculus, braid relations, and generalized cohomology

Bressler, Paul; Evens, Sam

doi:10.1090/S0002-9947-1990-0968883-2

The Schubert calculus, braid relations, and generalized cohomology
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by Paul Bressler and Sam Evens

Trans. Amer. Math. Soc. 317 (1990), 799-811

DOI: https://doi.org/10.1090/S0002-9947-1990-0968883-2

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Abstract:

Let $X$ be the flag variety of a compact Lie group and let ${h^{\ast }}$ be a complex-oriented generalized cohomology theory. We introduce operators on ${h^{\ast }}(X)$ which generalize operators introduced by Bernstein, Gel’fand, and Gel’fand for rational cohomology and by Demazure for $K$-theory. Using the Becker-Gottlieb transfer, we give a formula for these operators, which enables us to prove that they satisfy braid relations only for the two classical cases, thereby giving a topological interpretation of a theorem proved by the authors and extended by Gutkin.

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