2022/04/13 by Sergei Korotkikh, Korotkikh, Sergei · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2204.06166
openalex publication_date 2022/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish new properties of inhomogeneous spin q-Whittaker polynomials, which are symmetric polynomials generalizing t=0 Macdonald polynomials. We show that these polynomials are defined in terms of a vertex model, whose weights come not from an R-matrix, as is often the case, but from other intertwining operators of U'q(\mathfraksl2)-modules. Using this construction, we are able to prove a Cauchy-type identity for inhomogeneous spin q-Whittaker polynomials in full generality. Moreover, we are able to characterize spin q-Whittaker polynomials in terms of vanishing at certain points, and we find interpolation analogues of q-Whittaker and elementary symmetric polynomials.