Equivariant $K$-theory of flag varieties revisited and related results

Details Equivariant $K$-theory of flag varieties revisited and related results Equivariant $K$-theory of flag varieties revisited and related results

2011-01-31

arxiv.org/abs/1101.5911v2

Mathematics

Algebraic Geometry

Scientific paper

In this article we obtain many results on the multiplicative structure constants of $T$-equivariant Grothendieck ring of the flag variety $G/B$. We do this by lifting the classes of the structure sheaves of Schubert varieties in $K_{T}(G/B)$ to $R(T)\otimes R(T)$, where $R(T)$ denotes the representation ring of the torus $T$. We further apply our results to describe the multiplicative structure constants of $K(X)_{\mathbb Q}$ where $X$ is the wonderful compactification of the adjoint group of $G$, in terms of the structure constants of Schubert varieties in the Grothendieck ring of $G/B$.

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