Weak Bruhat interval modules of the 0-Hecke algebras for stable Grothendieck polynomials

Abstract

For a partition λ, let G_λ^(β) be the stable β-Grothendieck polynomial attached to λ. Each homogeneous component of the β= 1 specialization G_λ⁽¹⁾ is Schur-positive and hence positive in the fundamental basis of quasisymmetric functions. For m≥|λ|, let G_λ,m⁽¹⁾ be the homogeneous degree m component of G_λ⁽¹⁾. In this paper, we first give a direct proof of an expansion of G_λ,m⁽¹⁾ in the fundamental basis in terms of standard set-valued tableaux. We then use these tableaux as a basis to define a module of the $0$-Hecke algebra and show that the quasisymmetric characteristic of the resulting module is G_λ,m⁽¹⁾. We further show that this module decomposes as a direct sum of weak Bruhat interval modules.

The Zelevinsky involution, co-standard modules for quantum affine algebras and interval symmetric functions
Matheus Brito, Vyjayanthi Chari
arXiv3 Nov 2026PreprintCC BY 4.0Full textAlgebra & number theoryarXiv
Vexillary Grothendieck polynomials via bumpless pipe dreams
Elena S. Hafner
Discrete Mathematics14 May 2026Peer-reviewedLicence not statedFull text14 citedCombinatorics & discrete mathematicsOpenAlex
On the support of double Grothendieck polynomials
Yairon Cid-Ruiz
arXiv25 Sep 2026PreprintCC BY 4.0Full textAlgebra & number theoryarXiv
From Unit Interval Orders to Totally Nonnegative Matrices: Permanental Inequalities and Bruhat-Increasing Bijections
Sihong Pan, Mark Skandera, Jiayuan Wang
arXiv8 Oct 2026PreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
Quantum K-structure constants and cylindric Grothendieck polynomials for Grassmannians
Vassily Gorbounov, Christian Korff, Leonardo C. Mihalcea
arXiv22 Oct 2026PreprintarXiv licenceFull textAlgebra & number theory Combinatorics & discrete mathematicsarXiv

Cite

BibTeX RIS

BibTeX

@misc{kim2026weak,
  title = {{Weak Bruhat interval modules of the 0-Hecke algebras for stable Grothendieck polynomials}},
  author = {Young-Hun Kim},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10911},
  eprint = {2609.10911},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10911},
}

RIS

TY  - UNPB
TI  - Weak Bruhat interval modules of the 0-Hecke algebras for stable Grothendieck polynomials
AU  - Young-Hun Kim
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10911
UR  - https://arxiv.org/abs/2609.10911
AB  - For a partition λ, let G_λ^(β) be the stable β-Grothendieck polynomial attached to λ. Each homogeneous component of the β= 1 specialization G_λ^(1) is Schur-positive and hence positive in the fundamental basis of quasisymmetric functions. For m≥|λ|, let G_λ,m^(1) be the homogeneous degree m component of G_λ^(1). In this paper, we first give a direct proof of an expansion of G_λ,m^(1) in the fundamental basis in terms of standard set-valued tableaux. We then use these tableaux as a basis to define a module of the $0$-Hecke algebra and show that the quasisymmetric characteristic of the resulting module is G_λ,m^(1). We further show that this module decomposes as a direct sum of weak Bruhat interval modules.
ER  -

Abstract

Related

Cite