%0 Journal Article %T On C-small conjugacy classes in a reductive group %A G. Lusztig %J Mathematics %D 2010 %I arXiv %X Let G be an almost simple reductive group with Weyl group W. Let B be a Borel subgroup of G. Let C be an elliptic conjugacy class in W and let w be an element of minimal length of C. We investigate the existence of a semisimple class of G whose intersection with BwB has dimension dim(B). We show that in good characteristic such a semisimple class exists almost always. %U http://arxiv.org/abs/1005.4313v2