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PreprintCC BY 4.0arXiv

Kashiwara--Nakashima tableaux, Gelfand--Tsetlin patterns, and quantum symmetric pairs

  • Hideya Watanabe
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Abstract

Kashiwara--Nakashima tableaux and Gelfand--Tsetlin patterns of orthogonal type are famous as combinatorial models of the finite-dimensional irreducible representations of the special orthogonal Lie algebras soN. The former is constructed based on the representation theory of quantum groups, especially the theory of crystals, while the latter based on the branching rule for (soN,soN−1). In the present paper, we construct a natural bijection between them by means of the representation theory of quantum symmetric pairs corresponding to (soN,soN−1).

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Cite

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BibTeX
@misc{watanabe2026kashiwaranakashima,
  title = {{Kashiwara--Nakashima tableaux, Gelfand--Tsetlin patterns, and quantum symmetric pairs}},
  author = {Hideya Watanabe},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30780},
  eprint = {2608.30780},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30780},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Kashiwara--Nakashima tableaux, Gelfand--Tsetlin patterns, and quantum symmetric pairs
AU  - Hideya Watanabe
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30780
UR  - https://arxiv.org/abs/2608.30780
AB  - Kashiwara--Nakashima tableaux and Gelfand--Tsetlin patterns of orthogonal type are famous as combinatorial models of the finite-dimensional irreducible representations of the special orthogonal Lie algebras so_N. The former is constructed based on the representation theory of quantum groups, especially the theory of crystals, while the latter based on the branching rule for (so_N,so_N−1). In the present paper, we construct a natural bijection between them by means of the representation theory of quantum symmetric pairs corresponding to (so_N,so_N−1).
ER  -