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A proof of the Baum-Connes conjecture for real semisimple Lie groups with coefficients on flag varieties

We consider the equivariant K-theory of a real semisimple Lie group which acts on the (complex) flag variety of its complexification group. We construct an assemble map in the framework of KK-theory and then we prove that it is an isomorphism. The prove relies on a careful study of the orbits of the real group action on the flag variety and then piecing together different orbits. This result is a special case of the Baum-Connes conjecture with coefficients.

preprint2019arXivOpen access
Zhaoting Wei
math.RTmath.KT
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Zhaoting Wei

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