English

A conjectural Peterson isomorphism in K-theory

Algebraic Geometry 2017-05-10 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.1705.03435,
  title  = {A conjectural Peterson isomorphism in K-theory},
  author = {Thomas Lam and Changzheng Li and Leonardo C. Mihalcea and Mark Shimozono},
  journal= {arXiv preprint arXiv:1705.03435},
  year   = {2017}
}

Comments

15 pages

R2 v1 2026-06-22T19:41:58.821Z