A conjectural Peterson isomorphism in K-theory

Understand

We state a precise conjectural isomorphism between localizations of the equivariant quantum K-theory ring of a flag variety and the equivariant K-homology ring of the affine Grassmannian, in particular relating their Schubert bases and structure constants.

• This generalizes Peterson's isomorphism in (co)homology.
• We prove a formula for the Pontryagin structure constants in the K-homology ring, and we use it to check our conjecture in few situations.