  In a paper of 2003, B. K\"ulshammer, J. B. Olsson and G. R. Robinson defined
$\ell$-blocks for the symmetric groups, where $\ell >1$ is an arbitrary
integer, and proved that they satisfy an analogue of the Nakayama Conjecture.
Inspired by this work and the definitions of generalized blocks and sections
given by the authors, we give in this paper a definition of $d$-sections in the
finite general linear group, and construct $d$-blocks of unipotent characters,
where $d \geq 1$ is an arbitrary integer. We prove that they satisfy one
direction of an analogue of the Nakayama Conjecture, and, in some cases, prove
the other direction. We also prove that they satisfy an analogue of Brauer's
Second Main Theorem.
