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- W3094225569 abstract "We prove a localization theorem for affine $W$-algebras in the spirit of Beilinson--Bernstein and Kashiwara--Tanisaki. More precisely, for any non-critical regular weight $lambda$, we identify $lambda$-monodromic Whittaker $D$-modules on the enhanced affine flag variety with a full subcategory of Category $mathscr{O}$ for the $W$-algebra. To identify the essential image of our functor, we provide a new realization of Category $mathscr{O}$ for affine $W$-algebras using Iwahori--Whittaker modules for the corresponding Kac--Moody algebra. Using these methods, we also obtain a new proof of Arakawa's character formulae for simple positive energy representations of the $W$-algebra." @default.
- W3094225569 created "2020-10-29" @default.
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- W3094225569 date "2020-10-22" @default.
- W3094225569 modified "2023-09-25" @default.
- W3094225569 title "Localization for affine $W$-algebras" @default.
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- W3094225569 doi "https://doi.org/10.48550/arxiv.2010.11434" @default.
- W3094225569 hasPublicationYear "2020" @default.
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