Cells And Their Corresponding Representations Of The Weighted Coxeter Group （B₃,L）

We describe the cells of the weighted Coxeter group (B3, L), and study the corresponding representations of the associated Hecke algebra. According to the classification of the weight functions, we give an explicit expression for the Kazhdan-Lusztig basis elements cw of the Hecke algebra of type B3respectively in five different cases. Then we give the decomposition of the cells of the group B3and the matrix forms of the corresponding representations and study their reducibility. We calculate the a-values of the elements in the weighted Coxeter group (B3, L) by computing the product of the basis elements cw. As a result, we verify a series of conjectures of Lusztig in our case.