Abstract
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 Petersonâs varieties and show that Rietschâs conjecture about the total positivity holds for these cases.
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