A conjectural Peterson isomorphism in K-theory

Abstract

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.

arXiv comment15 pages

References in corpus (2)

• Richardson Varieties Have Kawamata Log Terminal Singularities
• A Chevalley formula for the equivariant quantum K-theory of cominuscule varieties

Cited by in corpus (2)

• On the quantum K-ring of the flag manifold
• A Pieri-type formula and a factorization formula for sums of $K$-$k$-Schur functions