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KO-rings of full flag varieties


Author: Marcus Zibrowius
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
Published electronically: July 24, 2014
MathSciNet review: 3301890
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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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Marcus Zibrowius
Affiliation: Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
Email: marcus.zibrowius@cantab.net

DOI: https://doi.org/10.1090/S0002-9947-2014-06318-6
Received by editor(s): May 29, 2013
Received by editor(s) in revised form: October 29, 2013
Published electronically: July 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society