Left Cells in the Affine Weyl Group of TypeC4

We find a representative set of left cells of the affine Weyl groupWaof typeC4as well as its left cell graphs by applying an algorithm. This algorithm was designed in my previous paper (Tôhoku J. Math.46,1994, 105–124). It is reformulated and improved in a more efficient form here. These representatives of left cells are presented as the vertices of so-called essential graphs so that the generalized τ-invariants of left cells ofWaare actually described explicitly, the latter almost characterize the left cells ofWa. Some comments and conjectures are proposed on cells of affine Weyl groups, mostly for the case of typeCl,l ≥ 2.