P-polynomials In Hecke Algebras With Unequal Parameters

In the paper,we mainly study some important contents of the Coxeter group representation and the related properties of the p-polynomia of the Dihedral group I2(m)in Hecke algebra with unequal parameters.The full text consists of four parts.Firstly,we give some prepare knowledge in the first chapter.Secondly,we introduce the properties of ?y,ws polynomial.In chapter three,we present the definitions and nature of r-polynomial and p-polynomial in Hecke algebra.Finally,based on the previous basic knowledge,we will find out the calculation formula of p-polynomial in Dihedral group I2(m)with l(w)-l(x)= 3.This article is based on the predecessors' research,so through this article,we can learn more about characters of Coxeter groups and multi-parameter Hecke-algebra.