68 citations · 670 across the 62 of their papers we have counts for
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Affine insertion and Pieri rules for the affine Grassmannian
Thomas Lam, Luc Lapointe, Jennifer Morse +1
We study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n,C). Our main results are: 1) Pieri rules for the Schubert bases of H^*(Gr…
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…
Demazure structure inside Kirillov-Reshetikhin crystals
Ghislain Fourier, Anne Schilling, Mark Shimozono
The conjecturally perfect Kirillov-Reshetikhin (KR) crystals are known to be isomorphic as classical crystals to certain Demazure subcrystals of crystal graphs of irreducible highe…
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…
Stable Grothendieck polynomials and K-theoretic factor sequences
Anders S. Buch, Andrew Kresch, Mark Shimozono +2
We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of stable Grothendieck polynomials for…
A Little bijection for affine Stanley symmetric functions
Thomas Lam, Mark Shimozono
David Little developed a combinatorial algorithm to study the Schur-positivity of Stanley symmetric functions and the Lascoux-Schützenberger tree. We generalize this algorithm to a…