Equivariant \(K\)-theory of flag varieties revisited and related results (Q2855855)

Let \(G\) be a semisimple simply connected algebraic group over an algebraically closed field. Let \(T\) be a maximal torus and let \(B\) be a Borel subgroup of \(G\) containing \(T\). Let \(X\) be the wonderful compactification of the adjoint group \(G/Z(G)\) of De Concini and Procesi.NEWLINENEWLINEIn a previous article [Transform. Groups 12, No. 2, 371--406 (2007; Zbl 1129.19003)] the author proved that the Grothendieck ring \(K(X)\) is a free \(K(G/B)\)-module and provided an explicit basis.NEWLINENEWLINEHere he constructs a different basis of \(K(X)\) with rational coefficients, as a free \(K(G/B)\)-module, lifting the Schubert classes in the \(T\)-equivariant Grothendieck ring \(K_T(G/B)\) to \(R(T)\otimes R(T)\), where \(R(T)\) is the representation ring of \(T\). The structure constants of this new basis are thus described in terms of the structure constants of the Schubert basis.