POLYNOMIAL SOLUTIONS TO THE WDVV EQUATIONS IN 4 DIMENSIONS

All polynomial solutions of the WDVV equations for the case n = 4 are determined. We find all five solutions predicted by Dubrovin, namely t hose corresponding to Frobenius structures on orbit spaces of finite C oxeter groups. Moreover we find two additional series of polynomial so lutions of which one series is of semi-simple type (massive). This res ult supports Dubrovin's conjecture if modified appropriately.