Auto-correlation functions for unitary groups

2021/10/01 by Kyu‐Hwan Lee, Se‐jin Oh, Lee, Kyu-Hwan +1
Mathematics · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Random Matrices and Applications #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2110.00505

openalex publication_date 2021/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the auto-correlations functions of order m≥ 1 for the characteristic polynomials of random matrices from certain subgroups of the unitary groups \U(2) and \U(3) by applying branching rules. These subgroups can be understood as analogs of Sato--Tate groups of \USp(4) in our previous paper. This computation yields symmetric polynomial identities with m-variables involving irreducible characters of \U(m) for all m ≥ 1 in an explicit, uniform way.

Related

• Unitary n-correlations with restricted support in random matrix theory
• In support of n-correlation
• Twisted moments of characteristic polynomials of random matrices in the unitary group
• The Schur Expansion of Characteristic Polynomials and Random Matrices
• Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N)