Lattice Points in the Newton Polytopes of Key Polynomials

Fan, Neil J. Y.; Guo, Peter L.; Peng, Simon C. Y.; Sun, Sophie C. C.

doi:10.1137/19m1305562

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…We explicate the argument alluded to in [ARY18,ARY19,ARY21]; we refer to these papers for definitions. This argument differs from the one in [FGPS20]. In [ARY21], it is shown that a lattice point β appears in the Schubitope associated to D(α) (rotated 90degrees clockwise) if and only if there exists T ∈ Tab(α) with content β.…”

Section: Polynomials and Sphericalitymentioning

confidence: 95%

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Classification of Levi-spherical Schubert varieties

Gao¹,

Hodges²,

Yong³

2021

Preprint

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A Schubert variety in the complete flag manifold GL n /B is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give a combinatorial classification of these Schubert varieties. This establishes a conjecture of the latter two authors, and a new formulation in terms of standard Coxeter elements. Our proof uses the theory of key polynomials (type A Demazure module characters).

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Section: Polynomials and Sphericalitymentioning

confidence: 95%

“…where c i = #{i ∈ T }. The following result is implicit in [ARY18, ARY19, ARY21] and explicit in [FGPS20].…”

Section: Polynomials and Sphericalitymentioning

confidence: 99%

Classification of Levi-spherical Schubert varieties

Gao¹,

Hodges²,

Yong³

2021

Preprint

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“…Partial order on weak compositions has been studied in [3,2,8,9]. In this section, we give a definition via the key tableau associated to the weak composition.…”

Section: Bruhat Order On Weak Compositionsmentioning

confidence: 99%

A Bijection Between K-Kohnert Diagrams and Reverse Set-Valued Tableaux

Pan,

2023

Electron. J. Combin.

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Lascoux polynomials are K-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux (RSVT) rule for Lascoux polynomials and reverse semistandard Young tableaux (RSSYT) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with RSSYT. Ross and Yong introduced K-Kohnert diagrams, which are analogues of Kohnert diagrams. They conjectured a K-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between RSVT and K-Kohnert diagrams.

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