Characters of unipotent groups over finite fields

Let G be a connected unipotent group over a finite field F(q). 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 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.