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PreprintCC BY 4.0arXiv

Temperley-Lieb Immanants of Ribbon Decomposition Matrices

  • Son Nguyen
  • Pavlo Pylyavskyy
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Abstract

Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices. We conjecture that this positivity holds for all elements of the dual canonical basis. This is known in the special case of Jacobi-Trudi matrices by a result of Haiman.

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Cite

BibTeXRIS
BibTeX
@misc{nguyen2026temperleylieb,
  title = {{Temperley-Lieb Immanants of Ribbon Decomposition Matrices}},
  author = {Son Nguyen and Pavlo Pylyavskyy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.12880},
  eprint = {2605.12880},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.12880},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Temperley-Lieb Immanants of Ribbon Decomposition Matrices
AU  - Son Nguyen
AU  - Pavlo Pylyavskyy
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2605.12880
UR  - https://arxiv.org/abs/2605.12880
AB  - Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices. We conjecture that this positivity holds for all elements of the dual canonical basis. This is known in the special case of Jacobi-Trudi matrices by a result of Haiman.
ER  -