PreprintarXiv licencearXiv
Demazure crystals for flagged set-valued reverse plane partitions
Abstract
In this paper, we build a Demazure crystal structure on the set of all flagged set-valued reverse plane partitions of a given skew shape λ/μ and flag Φ. Our construction provides a unified generalization of the Demazure crystal structures previously known for the set of all flagged semi-standard set-valued tableaux and the set of all flagged reverse plane partitions. Consequently, we obtain a combinatorial expansion for the flagged hybrid Grothendieck polynomial Hλ/μ(xΦ;t;w), introduced by Guo--Kang--Liu, in terms of key polynomials. Applying this expansion, we express the hybrid Grothendieck polynomial Hλ/μ(x;t;w) in terms of both the stable Grothendieck polynomials Gν(x) and the dual stable Grothendieck polynomials gν(x).
Related
- Models for dagger (∞,1)-categories III: Univalent flagged dagger (∞,1)-categories and unitarily complete dagger Segal anima
- Frayed Demazure weaves for Poisson-compatible cluster structures on Bott--Samelson charts
- Generalized parabolic Demazure modules and the N!/2-conjecture for two-row diagrams
- Quiver Demazure algebras I: Residue descent, finite quotients, and PBW bases
- Demazure Models of Algebraic Tori in Dimension 4
BibTeX
@misc{kundu2026demazure,
title = {{Demazure crystals for flagged set-valued reverse plane partitions}},
author = {Siddheswar Kundu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18151},
eprint = {2609.18151},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18151},
}
RIS
TY - UNPB
TI - Demazure crystals for flagged set-valued reverse plane partitions
AU - Siddheswar Kundu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18151
UR - https://arxiv.org/abs/2609.18151
AB - In this paper, we build a Demazure crystal structure on the set of all flagged set-valued reverse plane partitions of a given skew shape λ/μ and flag Φ. Our construction provides a unified generalization of the Demazure crystal structures previously known for the set of all flagged semi-standard set-valued tableaux and the set of all flagged reverse plane partitions. Consequently, we obtain a combinatorial expansion for the flagged hybrid Grothendieck polynomial H_λ/μ(x_Φ;t;w), introduced by Guo--Kang--Liu, in terms of key polynomials. Applying this expansion, we express the hybrid Grothendieck polynomial H_λ/μ(x;t;w) in terms of both the stable Grothendieck polynomials G_ν(x) and the dual stable Grothendieck polynomials g_ν(x).
ER -