Symmetries in the fourth Painleve equation and Okamoto polynomials

The fourth Painleve equation P-IV is known to have symmetry of the affine W eyl group of type A(2)((1)) with respect to the Backlund transformations. W e introduce a new representation of P-IV, called the symmetric form, by tak ing the three fundamental invariant divisors as the dependent variables. A complete description of the symmetry of P-IV is given in terms of this repr esentation. Through the symmetric form, it turns out that P-IV is obtained as a similarity reduction of the 3-reduced modified KP hierarchy. It is pro ved in particular that the special polynomials for rational solutions P-IV, called Okamoto polynomials, are expressible in terms of the 3-reduced Schu r functions.