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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The Schubert calculus, braid relations, and generalized cohomology
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by Paul Bressler and Sam Evens PDF
Trans. Amer. Math. Soc. 317 (1990), 799-811 Request permission

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
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 317 (1990), 799-811
  • MSC: Primary 57T15; Secondary 22E45, 32M10, 55N20
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0968883-2
  • MathSciNet review: 968883