Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type

Abstract

In this paper we calculate the Lagrangian Floer homology HF(L₀, L₁ : ℤ₂) of a pair of real forms (L₀, L₁) in a monotone Hermitian symmetric space M of compact type in the case where L₀ is not necessarily congruent to L₁. In particular, we have a generalization of the Arnold-Givental inequality in the case where M is irreducible. As its application, we prove that the totally geodesic Lagrangian sphere in the complex hyperquadric is globally volume minimizing under Hamiltonian deformations.