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arXiv · 2007.05697

Projective and Whittaker functors on category $\mathcal{O}$

Juan Camilo Arias·Erik Backelin
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Abstract

We show that the Whittaker functor on a regular block of the BGG-category $\mathcal{O}$ of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with Soergel and Mili\v{c}i\'{c}'s equivalence between the category of Whittaker modules and a singular block of $\mathcal{O}$. We show that the Whittaker functor is a quotient functor that commutes with all projective functors and endomorphisms between them.

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BibTeXRIS

Juan Camilo Arias, Erik Backelin. 2020-07-11. Projective and Whittaker functors on category $\mathcal{O}$. https://doi.org/10.1016/j.jalgebra.2021.01.024

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