A finite dimensional proof of the Verlinde formula

摘要

We prove two recurrence relations among dimensions Dg(r,d,ω):=dim H^0(UC,ω,ΘUC,ω)of spaces of generalized theta functions on the moduli spaces UC,ω.By using these recurrence relations,an explicit formula(the Verlinde formula)of Dg(r,d,ω)is proved(see Theorem 4.3).