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Applying the technique of p-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups SLn and PGLn, building on previous work of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the E-polynomial of the smooth moduli space of parabolic GLn-Higgs bundles is independent of the degree of the underlying vector bundles.
Shiyu Shen (Tue,) studied this question.