ERC Advanced Grant · 2024
Representation theory, equivariant topology and Langlands duality via fixed point schemes
We propose a three-way dictionary between representation theory of complex semisimple Lie groups, equivariant topology of affine Schubert varieties and mirror symmetry for Langlands dual Hitchin systems via the language of fixed point schemes. This unified framework will yield new insights and advances within these fields, with applications extending to other areas of mathematics and quantum physics. We introduce big algebras, which are commutative algebras attached to representations of complex semisimple Lie groups. We view them as commutative avatars of the representation because they bring together a wealth of sophisticated information, including a novel ring structure on multiplicity…
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