Character values at elements of order 2

In this paper we compute the character values of highest weight representations for classical groups of types A_n, B_n, C_n, D_n and the Exceptional group G_2 at all conjugacy classes of order 2. We prove that these character values, if nonzero, can be expressed either as a product involving the dimensions of two highest weight representations from classical subgroups, along with an additional constant term, or as an alternating sum of products of the dimensions of two highest weight representations from the classical subgroups, also accompanied by an extra constant term.