KO-rings of full flag varieties

Zibrowius, Marcus

doi:10.1090/S0002-9947-2014-06318-6

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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