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PreprintCC BY 4.0arXiv

Type B- and C- trigonometric weight functions

  • Kohei Motegi
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Abstract

We introduce and study trigonometric weight functions of type B and type C arising from integrable lattice models. These functions give q-deformations of the factorial K-theoretic Schur P- and Q-functions of Ikeda and Naruse, with the P-functions specialized to the type B case. We realize them as specializations of partition functions of a six-vertex model with triangular boundary conditions and derive their algebraic properties using the Yang-Baxter equation and properties of the R- and K-matrices. We introduce normalized weight functions and establish diagonal evaluation formulas, divisibility properties, and bounds on Newton polytopes analogous to those in type A, together with recursive relations and stability. We further derive branching formulas relating these functions to type A weight functions, and prove equal-cardinality orthogonality and all-cardinality biorthogonality relations.

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Cite

BibTeXRIS
BibTeX
@misc{motegi2026type,
  title = {{Type $B$- and $C$- trigonometric weight functions}},
  author = {Kohei Motegi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15344},
  eprint = {2610.15344},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15344},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Type B- and C- trigonometric weight functions
AU  - Kohei Motegi
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15344
UR  - https://arxiv.org/abs/2610.15344
AB  - We introduce and study trigonometric weight functions of type B and type C arising from integrable lattice models. These functions give q-deformations of the factorial K-theoretic Schur P- and Q-functions of Ikeda and Naruse, with the P-functions specialized to the type B case. We realize them as specializations of partition functions of a six-vertex model with triangular boundary conditions and derive their algebraic properties using the Yang-Baxter equation and properties of the R- and K-matrices. We introduce normalized weight functions and establish diagonal evaluation formulas, divisibility properties, and bounds on Newton polytopes analogous to those in type A, together with recursive relations and stability. We further derive branching formulas relating these functions to type A weight functions, and prove equal-cardinality orthogonality and all-cardinality biorthogonality relations.
ER  -