68 citations · 670 across the 62 of their papers we have counts for
5 papers · 1 filter
A conjectural Peterson isomorphism in K-theory
Thomas Lam, Changzheng Li, Leonardo C. Mihalcea +1
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 Grassm…
Quantum cohomology of G/P and homology of affine Grassmannian
Thomas Lam, Mark Shimozono
Let G be a simple and simply-connected complex algebraic group, P \subset G a parabolic subgroup. We prove an unpublished result of D. Peterson which states that the quantum cohomo…
Kempf collapsing and quiver loci
Allen Knutson, Mark Shimozono
Kempf [1976] studied proper, G-equivariant maps from equivariant vector bundles over flag manifolds to G-representations V, which he called _collapsings_. We give a simple formula…
Equivariant K-theory of affine flag manifolds and affine Grothendieck polynomials
Masaki Kashiwara, Mark Shimozono
We study the equivariant K-group of the affine flag manifold with respect to the Borel group action. We prove that the structure sheaf of the (infinite-dimensional) Schubert variet…
Four positive formulae for type A quiver polynomials
Allen Knutson, Ezra Miller, Mark Shimozono
We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and Fulton. All four formulae are combinatorial, in the sense that they are expressed in ter…