Reflection equations and Littlewood identities for spin Hall-Littlewood and $q$-Whittaker functions
Year: 2026
Type: preprint
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 $U_q(L\mathfrak{sl}_2)$-modules, as well as covectors stable under a $q$-Onsager coideal subalgebra.
Source: arXiv (Cornell University)
Authors: Gavrilova, Svetlana, Korotkikh, Sergei
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224097397