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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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KO-rings of full flag varieties
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by Marcus Zibrowius PDF
Trans. Amer. Math. Soc. 367 (2015), 2997-3016 Request permission

Abstract:

We present type-independent computations of the $\mathrm {KO}$-groups of full flag varieties, i.e. of quotient spaces $G/T$ of compact Lie groups by their maximal tori. Our main tool is the identification of the Witt ring, a quotient of the $\mathrm {KO}$-ring, of these varieties with the Tate cohomology of their complex $\mathrm {K}$-ring. The computations show that the Witt ring is an exterior algebra whose generators are determined by representations of $G$.
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Additional Information
  • Marcus Zibrowius
  • Affiliation: Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
  • MR Author ID: 946630
  • Email: marcus.zibrowius@cantab.net
  • Received by editor(s): May 29, 2013
  • Received by editor(s) in revised form: October 29, 2013
  • Published electronically: July 24, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 2997-3016
  • MSC (2010): Primary 55N15, 19L99
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06318-6
  • MathSciNet review: 3301890