Abstract
For a split maximal torus T of a split spin group \(G={{\mathrm {Spin}}}(n)\) over an arbitrary field, we consider the restriction homomorphism 
of the Chow rings of their classifying spaces with W the Weyl group of G. For \(n\le 6\), f is known to be surjective. For \(n\ge 7\), an obstruction for an element of 
to be in the image of f is given by the Steenrod operations on 
. Using it, we show that several standard generators of 
, including the defined for even n Euler class 
, are outside the image of f. This result differs from the analogues topological result.
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Author’s work has been supported by a Discovery Grant from the National Science and Engineering Research Council of Canada.
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This work has been accomplished during author’s stay at the Max–Planck Institute for Mathematics in Bonn.
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Karpenko, N.A. On Classifying Spaces of Spin Groups. Results Math 77, 144 (2022). https://doi.org/10.1007/s00025-022-01692-7
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DOI: https://doi.org/10.1007/s00025-022-01692-7