arXiv 1705.034352017-05-09math.AGmath.CO

A conjectural Peterson isomorphism in K-theory

Thomas Lam, Changzheng Li, Leonardo C. Mihalcea, Mark Shimozono

备注：: 15 pages

英文摘要：

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.

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