2016/12/11 by Mohammad Reza Rahmati, Rahmati, Mohammad Reza
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1612.03465
openalex publication_date 2016/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compare the context of Hodge structures with that of vertex algebras of conformal field theory. Vertex algebras appear as the highest weight representations of infinite dimensional Lie algebras. A correspondence between Higgs bundles and opers already is known as non-abelian Hodge theorem due to C. Simpson. The Beilinson-Bernstein localization (correspondence) also compares the context of variation of Hodge structure with that of highest weight modules over flag manifolds of semisimple Lie groups. A more general analogue of the Bernstein correspondence over a local manifold can also be formulted in the context of geometric Langlands correspondence. We discuss a generalized version of Harish-Chandra modules called Wakimoto modules and a generalized Harish-Chandra homomorphism. This text is mainly an expository discussion with a new insight toward the two concepts. We conclude with an explanation of geometric Langlands correspondence.