Moduli spaces of 1-dimensional semi-stable sheaves and strange duality on P2

We study Le Potier's strange duality conjecture on P2. We show the conjecture is true for the pair (W(2,0,2),M(d,0)) with d>0, where W(2,0,2) is the moduli space of semistable sheaves of rank 2, zero first Chern class and second Chern class 2, and M(d,0) is the moduli space of 1-dimensional semistable sheaves of first Chern class dH and Euler characteristic 0.