Verlinde/Grassmannian Correspondence and Rank 2 $\delta$-Wall-Crossing
Yongbin Ruan , Ming Zhang
Peking Mathematical Journal ›› 2022, Vol. 6 ›› Issue (1) : 217 -306.
Verlinde/Grassmannian Correspondence and Rank 2 $\delta$-Wall-Crossing
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.
Directorate for Mathematical and Physical Sciences(NSF grant DMS 1807079 and NSF FRG grant DMS 1564457)
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