Basic characters of the unitriangular group (for arbitrary primes)

Let U-n(q) denote the (upper) unitriangular group of degree n over the finite field F-q with q elements. In this paper we consider the basic (complex) characters of U-n(q) and we prove that every irreducible (complex) character of U-n(q) is a constituent of a unique basic character. This result extends a previous result which was proved by the author under the assumption p greater than or equal to n, where p is the characteristic of the field F-q.