Simon Pepin Lehalleur
The moduli spaces of Higgs bundles for the Langlands dual groups SL_n and PGL_n are related by a kind of mirror symmetry. In particular, there is an equality, conjectured by Hausel-Thaddeus and proved by Groechenig-Wyss-Ziegler, between their (orbifold) Hodge numbers. In joint work in progress with Victoria Hoskins, we show that this equality lifts to an isomorphism of motives. Our approach is based on the more recent proof by Maulik-Shen of the Hausel-Thaddeus conjecture together with our previous work on the motive of the moduli space of GL_n-Higgs bundles.