  Let G be a connected unipotent group over a finite field F_q with q elements.
In this article we propose a definition of L-packets of complex irreducible
representations of the finite group G(F_q) and give an explicit description of
L-packets in terms of the so-called "admissible pairs" for G. We then apply our
results to show that if the centralizer of every geometric point of G is
connected, then the dimension of every complex irreducible representation of
G(F_q) is a power of q, confirming a conjecture of V. Drinfeld. This paper is
the first in a series of three papers exploring the relationship between
representations of a group of the form G(F_q) (where G is a unipotent algebraic
group over F_q), the geometry of G, and the theory of character sheaves.
