Auto-correlation functions for unitary groups

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) to express them as sums of Schur functions of U(m). This computation yields new symmetric polynomial identities with m-variables involving Schur functions for all m ≥ 1 in an explicit, uniform way. 3⊗ w q 12 w b−q 13 ) = (−1) k v.