Solutions to WDVV from generalized Drinfeld-Sokolov hierarchies
  The dispersionless limit of generalized Drinfeld-Sokolov hierarchies associated to primitive regular conjugacy class of Weyl group W(g) is discussed. The map from these generalized Drinfeld - Sokolov hierarchies to algebraic solutions to WDVV equations has been constructed. Finite dimensional geometry behind hierarchies is studied.   Example of g=D_4 and [w]=D_4(a_1) is considered in details and corresponding Frobenius structure is found. 
Oleksandr Pavlyk