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

Tom 132 / 2013

Colloquium Mathematicum 132 (2013), 151-175 MSC: Primary 19L47; Secondary 14M15, 14L10. DOI: 10.4064/cm132-2-1

Streszczenie

We obtain several several results on the multiplicative structure constants of the $T$-equivariant Grothendieck ring $K_{T}(G/B)$ 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 $X$ denotes the wonderful compactification of the adjoint group of $G$, in terms of the structure constants of Schubert varieties in the Grothendieck ring of $G/B$.

Autorzy

• V. UmaDepartment of Mathematics