The notation d, l, and dl (for dextrorotatory and laevorotatory, respectively) is used to designate the sign of optical activity. According to Basic terminology of stereochemistry (IUPAC Recommendations 1996), this notation is obsolete and its usage is strongly discouraged. The recommended notation uses the prefixes (+), (−), and (±), respectively.
Since optical rotation is a distinguishing characteristic of enantiomers, the notation using d, l, and dl as well as the notation using (+), (−), and (±) can be used to distinguish the enantiomers of a chiral molecule. However, without further information, the absolute configuration (R or S) of the chiral molecule is indeterminable. Thus, it remains unknown whether the dextrorotatory enantiomer (d and (+), respectively) is the R enantiomer or the S enantiomer.
The notation D, L, and DL is based on the arbitrary convention according to which d-glyceraldehyde was named D-glyceraldehyde, l-glyceraldehyde was named L-glyceraldehyde, and the racemate dl-glyceraldehyde was named DL-glyceraldehyde. (Note that the stereodescriptors D, L, and DL shall actually be written in small capitals, which cannot be correctly typeset here.) The enantiomers were taken to have the absolute configuration represented by the Fischer projection.
Today, we know that D-(+)-glyceraldehyde actually is (2R)-2,3-dihydroxypropanal.