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 Verl...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).展开更多
Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of ...Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of invariants by imposing different stability conditions on the gauged linear sigma model associated with the Grassmannian.We construct two families of stability conditions connecting the two theories and prove two wall-crossing results.We confirm the Verlinde/Grassmannian correspondence in the rank two case.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11831013 and 11921001)supported by National Natural Science Foundation of China(Grant No.11501154)Natural Science Foundation of Zhejiang Province(Grant No.LQ16A010005)。
文摘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).
基金The bulk of this work was done during the first author’s tenure at University of Michigan and he was partially supported by NSF grant DMS 1807079 and NSF FRG grant DMS 1564457.
文摘Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of invariants by imposing different stability conditions on the gauged linear sigma model associated with the Grassmannian.We construct two families of stability conditions connecting the two theories and prove two wall-crossing results.We confirm the Verlinde/Grassmannian correspondence in the rank two case.
