Determination of the Characteristic Class Functions of the Weyl Group of type G_2

In this paper, our main objective is to combinatorially obtain all characteristic class functions of the Weyl group of type G_2 with the help of the structure of generalized descent algebra including Solomon’s descent algebra and Mantaci-Reutenauer algebra. We also give an interpretation of the character table of the Weyl group of type G_2 in terms of the permutation characters defined on the set of cosets belonging to each of its some special subgroups.