2024/10/18 by Pierre-Antoine Bernard, Bernard, Pierre-Antoine, Abderahmane Bouziane +13
Mathematics · #33D45 #33D80 #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2410.14856
openalex publication_date 2024/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of q-Hahn type is provided. The approach relies on the meta q-Hahn algebra and its finite-dimensional bidiagonal representations. The functions of q-Hahn type are identified as overlaps (up to global factors) between bases solving ordinary or generalized eigenvalue problems in the representation of the meta q-Hahn algebra. Moreover, (bi)orthogonality relations, recurrence relations, difference equations and some contiguity relations satisfied by these functions are recovered algebraically using the actions of the generators of the meta q-Hahn algebra on various bases.