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Reflection equations and Littlewood identities for spin Hall-Littlewood and q-Whittaker functions

  • Svetlana Gavrilova
  • Sergei Korotkikh
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Abstract

We describe two-parametric Littlewood identities for inhomogeneous stable spin Hall-Littlewood and inhomogeneous spin q-Whittaker symmetric functions. These identities generalize the Littlewood identity found by Warnaar (2006) for the ordinary Hall-Littlewood polynomials. However, instead of Rogers-Szegö coefficients used by Warnaar, coefficients in our identities are given by products of Al-Salam-Chihara polynomials. Our proof relies on integrable lattice models. A key step includes three new solutions to the reflection and boundary equations for the fully fused six-vertex model. To find these solutions we use isomorphisms between tensor products of evaluation Uq(Lsl2)-modules, as well as covectors stable under a q-Onsager coideal subalgebra.

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Cite

BibTeXRIS
BibTeX
@misc{gavrilova2026reflection,
  title = {{Reflection equations and Littlewood identities for spin Hall-Littlewood and $q$-Whittaker functions}},
  author = {Svetlana Gavrilova and Sergei Korotkikh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36644},
  eprint = {2610.36644},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36644},
}
RIS
TY  - UNPB
TI  - Reflection equations and Littlewood identities for spin Hall-Littlewood and q-Whittaker functions
AU  - Svetlana Gavrilova
AU  - Sergei Korotkikh
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36644
UR  - https://arxiv.org/abs/2610.36644
AB  - We describe two-parametric Littlewood identities for inhomogeneous stable spin Hall-Littlewood and inhomogeneous spin q-Whittaker symmetric functions. These identities generalize the Littlewood identity found by Warnaar (2006) for the ordinary Hall-Littlewood polynomials. However, instead of Rogers-Szegö coefficients used by Warnaar, coefficients in our identities are given by products of Al-Salam-Chihara polynomials. Our proof relies on integrable lattice models. A key step includes three new solutions to the reflection and boundary equations for the fully fused six-vertex model. To find these solutions we use isomorphisms between tensor products of evaluation U_q(Lsl_2)-modules, as well as covectors stable under a q-Onsager coideal subalgebra.
ER  -