2025/05/02 by Sean Howe, Howe, Sean
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2505.01205
openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
For X a pre-λ random variable, we show the σ-moment generating function of -X can be obtained from the σ-moment generating function of X by applying the composition of the standard and degree flip involutions on symmetric power series. This isometric involution is natural as it preserves the pre-λ ring structure on symmetric power series with pre-λ coefficients, thus this formula provides a simple description of the σ-moment generating function of -X whenever the σ-moment generating function of X has a simple description using the pre-λ structure. As an application we compute, in a natural range, the dimensions of orthogonal and symplectic group invariants in tensor products of exterior powers of their standard representations on ℂn. We also compute a generating function for stable traces of Frobenius related to the moment conjecture for prime-order function field Dirichlet characters.