Cellular Basis Of Hecke Algebra Of Dihedral Type

In this paper we construct an explicit cellular basis for the Hecke algebra associated to the dihedral groups I2(n)of order 2n and defined over R by using linear combinations of some Kazhdan-Lusztig bases with coefficients given by certain evaluations of Sk,R(n)or Sk,R(x)where R is a Z[1/n,2 cos(2π/n),u±1/2]-algebra.Under the assumption that(charF,2m+1)=1.we show that Sm,F(x)has no multiple roots in any one of its splitting fields.In this case,we construct an explicit cellular basis for the Hecke algebra associated to the dihedral groups I2(n)of order 2n=2(2m+1).Under the assumption that(charF,2m)=1.we show that Sm-1,F(x)has no multiple roots in any one of its splitting fields.In this case,we construct an explicit cellular basis for the Hecke algebra associated to the dihedral groups I2(n)of order 2n=2(2m).