On soliton equations of exceptional type (Q1330073)

The explicit structure of soliton equations in bilinear form is studied. The equations studied are those corresponding to A-D-E-type Kac-Moody algebra in the basic representation \(L(\Lambda_ 0)\), with principal or homogeneous realization. Using results of Kac-Wakimoto, describing these equations with a generalized Casimir operator, the author is able to write the equations even more explicitly in terms of Schur polynomials. Similar results are also given for the BKP hierarchy.