Quantum cohomology rings of Lagrangian and orthogonal Grassmannians and total positivity
Quantum cohomology rings of Lagrangian and orthogonal Grassmannians and total positivity
We verify in an elementary way a result of Peterson for the maximal orthogonal and Lagrangian Grassmannians, and then find Vafa-Intriligator type formulas which compute their $3$-point, genus zero Gromov-Witten invariants. Finally we study the total positivity of the related Peterson's varieties and show that Rietsch's conjecture about the total …