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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Schubert calculus, braid relations, and generalized cohomology


Authors: Paul Bressler and Sam Evens
Journal: Trans. Amer. Math. Soc. 317 (1990), 799-811
MSC: Primary 57T15; Secondary 22E45, 32M10, 55N20
MathSciNet review: 968883
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0968883-2
PII: S 0002-9947(1990)0968883-2
Article copyright: © Copyright 1990 American Mathematical Society