Abstract
Let G/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimensions, for an integer k we can define the Adams map of type k to be l k : H*(G/P, ℚ) → H*(G/P, ℚ), l k (u) = k i u, u ∈ H 2i(G/P, ℚ). We show that if k is prime to the order of the Weyl group of G, then l k can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary.
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Lin, X.Z. Geometric realization of Adams maps. Acta. Math. Sin.-English Ser. 27, 863–870 (2011). https://doi.org/10.1007/s10114-011-0164-y
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DOI: https://doi.org/10.1007/s10114-011-0164-y