Quantum cohomology rings of Lagrangian and orthogonal Grassmannians and total positivity

Cheong, Daewoong

doi:10.1090/S0002-9947-09-04720-5

Quantum cohomology rings of Lagrangian and orthogonal Grassmannians and total positivity
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Trans. Amer. Math. Soc. 361 (2009), 5505-5537 Request permission

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 Peterson’s varieties and show that Rietsch’s conjecture about the total positivity holds for these cases.

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