# Tagged Questions

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### Equivariant $K$-theory, singular vectors, and flag manifolds

For a homogeneous space $M = G/B$, with $G$ a (complex) semi-simple Lie group, it is very well-known that equivariant vector bundles $E$ over $M$ correspond to representations $(V_{\lambda},\lambda)$ ...

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### How to deduce (8.1) in Lusztig's “Equivariant K-theory and representations of Hecke Algebras”

Let G be a connected complex algebraic group G and X=G/B, where B is the Borel subgroup. $ M=G\times C^{*}$, where $C^*$ acts on X trivially. Let $K_M(X)$ be the equivariant K-theory. Let $s\in S$ be ...

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### The proof of the splitting principle in equivariant K-theory via flag manifolds

In Atiyah's famous paper "Bott periodicity and the index of elliptic operators" section 4, he proved the splitting principle for unitary groups (Propostion 4.9 in that paper), namely:
Let $j: ...