2021/12/03 by Roger Van Peski, Van Peski, Roger · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR) #Random Matrices and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2112.02147
openalex publication_date 2021/12/03 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
We prove that the boundary of the Hall-Littlewood t-deformation of the Gelfand-Tsetlin graph is parametrized by infinite integer signatures, extending results of Gorin and Cuenca on boundaries of related deformed Gelfand-Tsetlin graphs. In the special case when 1/t is a prime p we use this to recover results of Bufetov-Qiu and Assiotis on infinite p-adic random matrices, placing them in the general context of branching graphs derived from symmetric functions. Our methods rely on explicit formulas for certain skew Hall-Littlewood polynomials. As a separate corollary to these, we obtain a simple expression for the joint distribution of the cokernels of products A1, A2A1, A3A2A1,… of independent Haar-distributed matrices Ai over the p-adic integers ℤp. This expression generalizes the explicit formula for the classical Cohen-Lenstra measure on abelian p-groups.