52 citations · 61 across the 10 of their papers we have counts for
8 papers · 1 filter
Shuffle formula in science fiction for Macdonald polynomials
Donghyun Kim, Seung Jin Lee, Jaeseong Oh
We initiate the study of the Macdonald intersection polynomials , which are indexed by -tuples of partitions $μ^{(1)},\dots,μ^{(…
Toward Butler's conjecture
Donghyun Kim, Seung Jin Lee, Jaeseong Oh
For a partition , let be two distinct partitions such that . Butler conjectured that the divided difference $\operatorname{I}_{λ,μ}[X;q,t]=(T_λ\w…
Haglund's conjecture for multi- Macdonald polynomials
Seung Jin Lee, Jaeseong Oh, Brendon Rhoades
We provide new approaches to prove identities for the modified Macdonald polynomials via their LLT expansions. As an application, we prove a conjecture of Haglund concerning the mu…
Explicit formulas for e-positivity of chromatic quasisymmetric functions
Seung Jin Lee, Sue Kyong Y. Soh
In 1993, Stanley and Stembridge conjectured that a chromatic symmetric function of any -free poset is -positive. Guay-Paquet reduced the conjecture to - and $(2+2)…
On the coproduct in affine Schubert calculus
Thomas Lam, Seung Jin Lee, Mark Shimozono
The cohomology of the affine flag variety of a complex reductive group is a comodule over the cohomology of the affine Grassmannian. We give positive formulae for the coproduct of…
Back stable Schubert calculus
Thomas Lam, Seung Jin Lee, Mark Shimozono
We study the back stable Schubert calculus of the infinite flag variety. Our main results are: 1) a formula for back stable (double) Schubert classes expressing them in terms of a…
Combinatorial description of the cohomology of the affine flag variety
Seung Jin Lee
We construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigate the combinatorics of affine Schubert calculus for type . We introduce…
Pieri rule for the affine flag variety
Seung Jin Lee
We prove the affine Pieri rule for the cohomology of the affine flag variety conjectured by Lam, Lapointe, Morse and Shimozono. We study the cap operator on the affine nilHecke rin…