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

V. Uma¹

¹ Department of Mathematics IIT Madras Chennai, India

Colloquium Mathematicum, Tome 132 (2013) no. 2, pp. 151-175

Résumé

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 $G/B$.

Détail

DOI : 10.4064/cm132-2-1

Keywords: obtain several several results multiplicative structure constants t equivariant grothendieck ring flag variety lifting classes structure sheaves schubert varieties otimes where denotes representation ring torus nbsp further apply results describe multiplicative structure constants mathbb where denotes wonderful compactification adjoint group nbsp terms structure constants schubert varieties grothendieck ring