  We consider word maps and word maps with constants on a simple algebraic
group. We present results on the images of such maps, in particular, we prove a
theorem on the dominance of general word maps with constants, which can be
viewed as an analogue of a well-known theorem of Borel on the dominance of
genuine word maps. Besides, we establish a relationship between the existence
of unipotents in the image of a word map and the structure of the corresponding
representation variety.

Group Theory