Related papers: Demazure crystals for Kohnert polynomials

We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools…

Schubert polynomials were introduced in the context of the geometry of flag varieties. This paper investigates some of the connections not yet understood between several combinatorial structures for the construction of Schubert polynomials;…

Schubert polynomials are a basis for the polynomial ring that represent Schubert classes for the flag manifold. In this paper, we introduce and develop several new combinatorial models for Schubert polynomials that relate them to other…

We present the first positive combinatorial rule for expanding the product of a permuted-basement Demazure atom and a Schur polynomial. Special cases of permuted-basement Demazure atoms include Demazure atoms and characters. These cases…

For any Coxeter system, and any double coset for two standard parabolic subgroups, we introduce a Demazure operator. These operators form a basis for morphism spaces in a category we call the nilCoxeter category, and we also present this…

The flagged refined stable Grothendieck polynomials of skew shapes generalize several polynomials like stable Grothendieck polynomials, flagged skew Schur polynomials. In this paper, we provide a combinatorial expansion of the flagged…

Our previous work introduced a category of extended queer crystals, whose connected normal objects have unique highest weight elements and characters that are Schur $Q$-polynomials. The initial models for such crystals were based on…

Kohnert proposed the first monomial positive formula for Schubert polynomials as the generating polynomial for certain unit cell diagrams obtained from the Rothe diagram of a permutation. Billey, Jockusch and Stanley gave the first proven…

This paper studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating monomial and an atom, which was an open…

We give a parametrization for crystal bases of Demazure modules as a set of lattice points in some convex polytope and we also describe explicitly the extremal vectors as solutions of some system of linear equations.

We examine the non-symmetric Macdonald polynomials $E_\lambda(x;q,t)$ at $q=1$, as well as the more general permuted-basement Macdonald polynomials. When $q=1$, we show that $E_\lambda(x;1,t)$ is symmetric and independent of $t$ whenever…

We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating…

We consider the varieties of singular $m \times m$ complex matrices which may be either general, symmetric or skew-symmetric (with $m$ even). For these varieties we have shown in another paper that they had compact "model submanifolds", for…

Lascoux has given a triangular version of the Cauchy identity where Schur polynomials are replaced by Demazure characters and Demazure atoms. He has then used the staircase expansion to recover expansions for all Ferrers shapes, where the…

Recently, Gross, Mansour and Tucker introduced the partial duality polynomial of a ribbon graph and posed a conjecture that there is no orientable ribbon graph whose partial duality polynomial has only one non-constant term. We found an…

We study certain faces of the normal polytope introduced by Feigin, Littelmann and the author whose lattice points parametrize a monomial basis of the PBW-degenerated of simple modules for $\mathfrak{sl}_{n+1}$. We show that lattice points…

We generalize a theorem of Littlewood concerning the factorization of Schur polynomials when their variables are twisted by roots of unity. We show that a certain family of flagged skew Schur polynomials admit a similar factorization. These…

We use deformations and mutations of scattering diagrams to show that the coefficients of a scattering diagram with initial functions $f1 = (1+tx)^{\mu}$ and $f2 = (1+ty)^{\nu}$ are polynomial in ${\mu}$, ${\nu}$ and non-trivial in a…

We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. We then discuss a family of polynomials…

It has previously been shown that, at least for non-exceptional Kac-Moody Lie algebras, there is a close connection between Demazure crystals and tensor products of Kirillov-Reshetikhin crystals. In particular, certain Demazure crystals are…