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A conjectural Peterson isomorphism in \(K\)-theory. (English) Zbl 1423.14278
Summary: 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.

MSC:
14M15 Grassmannians, Schubert varieties, flag manifolds
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
19L47 Equivariant \(K\)-theory
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