Left Cells Of Affine Weyl Groups Of (?)₇ With A=7

Left,right and two-sided cells of a Coxeter group were introduced by Kazhdan and Lusztig in 1979,which plays an important role in the representations of Hecke algebras and algebra groups.In this paper ,we use Shi's algorithm to describe all the left cells in the two-sided cellsΩof the affine Weyl group (?)₇ with a(Ω)= 7 by finding a representative set of left cells inΩ. and by drawing all the corresponding left cell graphs. Then we work out all the distinguished involutions in these two-sided cells .