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- W4287324798 abstract "We introduce a class of equivalences, which we call generalized semi-infinite Hecke equivalences, between certain categories of representations of graded associative algebras which appear in the setting of semi-infinite cohomology for associative algebras and categories of representations of related algebras of Hecke type which we call semi-infinite Hecke algebras. As an application we obtain an equivalence between a category of representations of a non-twisted affine Lie algebra $widehat{mathfrak g}$ of level $-2h^vee-k$, where $h^vee$ is the dual Coxeter number of the underlying semisimple Lie algebra $mathfrak g$ and $kin mathbb{C}$, and the category of finitely generated representations of the W-algebra associated to $widehat{mathfrak g}$ of level $k$. When $k=-h^vee$ this yields an equivalence between a category of representations of $widehat{mathfrak g}$ of central charge $-h^vee$ and the category ${rm Coh}({rm Op}_{^LG}(D^times))$ of coherent sheaves on the space ${rm Op}_{^LG}(D^times)$ of $^LG$-opers on the punctured disc $D^times$, where $^LG$ is the Langlands dual group to the algebraic group of adjoint type with Lie algebra $mathfrak g$. This can be regarded as a version of the local geometric Langlands correspondence. The above mentioned equivalences generalize to the case of affine Lie algebras the Skryabin equivalence between the categories of generalized Gelfand-Graev representations of $mathfrak g$ and the categories of representations of the corresponding finitely generated W-algebras, and Kostant's results on the classification of Whittaker modules over $mathfrak g$." @default.
- W4287324798 created "2022-07-25" @default.
- W4287324798 creator A5016517002 @default.
- W4287324798 date "2021-02-22" @default.
- W4287324798 modified "2023-09-24" @default.
- W4287324798 title "A generalized semi-infinite Hecke equivalence and the local geometric Langlands correspondence" @default.
- W4287324798 doi "https://doi.org/10.48550/arxiv.2102.11247" @default.
- W4287324798 hasPublicationYear "2021" @default.
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