Unipotent Elements, Standard Involutions, and the Divisor Matrix

Abstract

We give an explicit description of a matrix T(n) in GL n (ℤ) with the property that T(n) = T(n)−1 and , where D n = (d ij ) is the divisor matrix whose (i,j)-entry is For all n ∈ ℕ, the matrices D n and T(n) are obtained as the truncations of semi-infinite matrices D and T also satisfying the relations T = T −1 and T D T −1 = D −1. By encoding the entries of the ith row of the semi-infinite matrix T in a Dirichlet series we give a description of the coefficients of T.