68 citations · 670 across the 62 of their papers we have counts for
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From double quantum Schubert polynomials to k-double Schur functions via the Toda lattice
Thomas Lam, Mark Shimozono
We show that the k-double Schur functions defined by the authors, and the quantum double Schubert polynomials studied by Kirillov and Maeno and by Ciocan-Fontanine and Fulton, can…
Quantum double Schubert polynomials represent Schubert classes
Thomas Lam, Mark Shimozono
The quantum double Schubert polynomials studied by Kirillov and Maeno, and by Ciocan-Fontanine and Fulton, are shown to represent Schubert classes in Kim's presentation of the equi…
Equivariant Pieri Rule for the homology of the affine Grassmannian
Thomas Lam, Mark Shimozono
An explicit rule is given for the product of the degree two class with an arbitrary Schubert class in the torus-equivariant homology of the affine Grassmannian. In addition a Pieri…
k-Double Schur functions and equivariant (co)homology of the affine Grassmannian
Thomas Lam, Mark Shimozono
The Schubert bases of the torus-equivariant homology and cohomology rings of the affine Grassmannian of the special linear group are realized by new families of symmetric functions…
X = K under review
Cedric Lecouvey, Masato Okado, Mark Shimozono
We review the X = K conjecture and important ingredients for the proof. We also attach notes on the rank estimate for the X = K theorem to hold and on the strange relation that was…