Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

Abstract

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 $G/B$.