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PreprintarXiv licencearXiv

Lower and upper bounds of Schur characters

  • Zhuowei Lin
  • Candice X. T. Zhang
  • Zhong-Xue Zhang
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Abstract

Characterizations of lower and upper bounds for dual characters of flagged Weyl modules have attracted considerable interest. In this paper, we establish explicit pattern avoidance characterizations for lower and upper bounds of Schur characters, namely, the dual characters of Weyl modules associated with arbitrary diagrams. This setting extends the corresponding extremal problems for dual characters of flagged Weyl modules and includes skew Schur polynomials and, through Rothe diagrams, Stanley symmetric functions. Specifically, for a permutation w, we show that the Stanley symmetric function Fw attains the lower bound if and only if w avoids $321,2143,2413,3142$, and $3412$, and attains the upper bound if and only if w avoids $312$ and $321$.

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Cite

BibTeXRIS
BibTeX
@misc{lin2026lower,
  title = {{Lower and upper bounds of Schur characters}},
  author = {Zhuowei Lin and Candice X. T. Zhang and Zhong-Xue Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02050},
  eprint = {2609.02050},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02050},
}
RIS
TY  - UNPB
TI  - Lower and upper bounds of Schur characters
AU  - Zhuowei Lin
AU  - Candice X. T. Zhang
AU  - Zhong-Xue Zhang
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02050
UR  - https://arxiv.org/abs/2609.02050
AB  - Characterizations of lower and upper bounds for dual characters of flagged Weyl modules have attracted considerable interest. In this paper, we establish explicit pattern avoidance characterizations for lower and upper bounds of Schur characters, namely, the dual characters of Weyl modules associated with arbitrary diagrams. This setting extends the corresponding extremal problems for dual characters of flagged Weyl modules and includes skew Schur polynomials and, through Rothe diagrams, Stanley symmetric functions. Specifically, for a permutation w, we show that the Stanley symmetric function F_w attains the lower bound if and only if w avoids $321,2143,2413,3142$, and $3412$, and attains the upper bound if and only if w avoids $312$ and $321$.
ER  -